Revision History for A155170
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#12 by Michel Marcus at Mon Feb 08 05:18:40 EST 2021
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#11 by Joerg Arndt at Mon Feb 08 02:52:58 EST 2021
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#10 by Michel Marcus at Mon Feb 08 02:13:52 EST 2021
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#9 by Michel Marcus at Mon Feb 08 02:13:47 EST 2021
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| COMMENTS
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Row sums are: {: 1, 2, 2, -4, -52, -412, -3292, -28492, -270412, -2810572, -31840972, ...}., ...
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| STATUS
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proposed
editing
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#8 by G. C. Greubel at Sun Feb 07 23:34:43 EST 2021
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#7 by G. C. Greubel at Sun Feb 07 23:34:37 EST 2021
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#6 by G. C. Greubel at Sun Feb 07 23:33:23 EST 2021
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| NAME
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Triangle T(n,m)= m, k) = k! - n! + (n-mk)! read by rows, 0<=m<=n.
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| DATA
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1, 1, 1, 1, 0, 1, 1, -3, -3, 1, 1, -17, -20, -17, 1, 1, -95, -112, -112, -95, 1, 1, -599, -694, -708, -694, -599, 1, 1, -4319, -4918, -5010, -5010, -4918, -4319, 1, 1, -35279, -39598, -40194, -40272, -40194, -39598, -35279, 1, 1, -322559, -357838, -362154, -362736, -362736, -362154, -357838, -322559, 1
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| COMMENTS
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Row sums are : {1, 2, 2, -4, -52, -412, -3292, -28492, -270412, -2810572, -31840972,..., ...}.
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| LINKS
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G. C. Greubel, <a href="/A155170/b155170.txt">Rows n = 0..100 of the triangle, flattened</a>
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| FORMULA
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sumSum_{mk=0..n} T(n,, m) = 2*A003422(n+1)-) - A000142(n+1). - ). - _R. J. Mathar, _, Jun 24 2011
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| EXAMPLE
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Triangle begins as:
1;
1, , 1;
1, , 0, , 1;
1, -, -3, -, -3, , 1;
1, -, -17, -, -20, -, -17, , 1;
1, -, -95, -, -112, -, -112, -, -95, , 1;
1, -, -599, -, -694, -, -708, -, -694, -, -599, , 1;
1, -, -4319, -, -4918, -, -5010, -, -5010, -, -4918, -, -4319, , 1;
1, -, -35279, -, -39598, -, -40194, -, -40272, -, -40194, -, -39598, -, -35279, , 1;
1, -322559, -357838, -362154, -362736, -362736, -362154, -357838, -322559, 1;
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| MATHEMATICA
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Table[Table[ m! - k! -n! + (-m + ! +(n-k)!, {m, 0, n}], {n, 0, 12}, {k, 0, 10}]; n}]//Flatten
Flatten[%]
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| PROG
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(Sage) f=factorial; flatten([[f(n-k) -f(n) +f(k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 07 2021
(Magma) F:=Factorial;; [F(n-k) -F(n) +F(k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 07 2021
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| CROSSREFS
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Cf. A176151, A176152.
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| STATUS
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approved
editing
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#5 by Russ Cox at Fri Mar 30 17:34:32 EDT 2012
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| AUTHOR
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_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Jan 21 2009
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Discussion
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| Fri Mar 30
| 17:34
| OEIS Server: https://oeis.org/edit/global/158
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#4 by Joerg Arndt at Fri Jun 24 11:07:15 EDT 2011
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#3 by R. J. Mathar at Fri Jun 24 09:58:12 EDT 2011
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