Revision History for A183205
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#7 by Andrey Zabolotskiy at Sat Apr 23 16:21:30 EDT 2022
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#6 by Andrey Zabolotskiy at Sat Apr 23 16:21:26 EDT 2022
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| NAME
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a(n) = [x^n] (1-x)^(3n+1)/(n+1) * Sum_{k>=0} C(n+k-1,k)^3*x^k.
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| FORMULA
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a(n) = A183204(n)/(n+1), where A183204 equals the central terms of triangle A181544.
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| PROG
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((PARI) {a(n)=polcoeff((1-x)^(3*n+1)/(n+1)*sum(j=0, 2*n, binomial(n+j, j)^3*x^j), n)}
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| CROSSREFS
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Cf. A181544, A183204.
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| STATUS
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approved
editing
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#5 by Russ Cox at Fri Mar 30 18:37:23 EDT 2012
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| AUTHOR
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_Paul D. Hanna (pauldhanna(AT)juno.com), _, Dec 30 2010
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Discussion
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| Fri Mar 30
| 18:37
| OEIS Server: https://oeis.org/edit/global/213
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#4 by T. D. Noe at Thu Dec 30 12:36:19 EST 2010
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#3 by Joerg Arndt at Thu Dec 30 04:33:16 EST 2010
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#2 by Paul D. Hanna at Thu Dec 30 03:56:22 EST 2010
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allocated for Paul D. Hanna
a(n) = [x^n] (1-x)^(3n+1)/(n+1) * Sum_{k>=0} C(n+k-1,k)^3*x^k.
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| DATA
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1, 2, 16, 190, 2768, 45584, 814728, 15439974, 305760400, 6265985440, 131980086368, 2843029539376, 62400628835608, 1391503990134080, 31454839290752912, 719470742267557110, 16627360903974831120, 387786053931422003360
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| OFFSET
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0,2
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| FORMULA
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a(n) = A183204(n)/(n+1), where A183204 equals the central terms of triangle A181544.
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| PROG
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(PARI) {a(n)=polcoeff((1-x)^(3*n+1)/(n+1)*sum(j=0, 2*n, binomial(n+j, j)^3*x^j), n)}
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| CROSSREFS
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Cf. A181544, A183204.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 30 2010
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| STATUS
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approved
proposed
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#1 by Paul D. Hanna at Thu Dec 30 03:48:42 EST 2010
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| NAME
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allocated for Paul D. Hanna
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| KEYWORD
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allocated
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| STATUS
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approved
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