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A155170
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Triangle T(n, k) = k! - n! + (n-k)! read by rows.
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3
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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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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FORMULA
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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[k! -n! +(n-k)!, {n, 0, 12}, {k, 0, n}]//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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KEYWORD
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AUTHOR
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STATUS
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approved
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