A098470 Form array in which n-th row is obtained by expanding (1+x+x^2)^n and taking the 5th column from the center.
1, 6, 28, 112, 414, 1452, 4917, 16236, 52624, 168168, 531531, 1665456, 5182008, 16031952, 49366674, 151419816, 462919401, 1411306358, 4292487562, 13029127584, 39478598170, 119439969220, 360881425710, 1089126806040
Offset: 5
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 5..1005
- Eric Weisstein's World of Mathematics, Trinomial Coefficient
Programs
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Maple
# Assuming offset 0: a := n -> simplify(GegenbauerC(n, -n-5, -1/2)): seq(a(n), n=0..25); # Peter Luschny, May 09 2016
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Mathematica
Table[GegenbauerC[n, -n - 5, -1/2], {n,0,50}] (* G. C. Greubel, Feb 28 2017 *) -
PARI
x='x + O('x^50); Vec(32*x^5/(sqrt((1+x)*(1-3*x))*(1-x-sqrt((1+x)*(1-3*x)))^5)) \\ G. C. Greubel, Feb 28 2017
Formula
(n^2-25)*a(n) = n*(2*n-1)*a(n-1) + 3*n*(n-1)*a(n-2). - Vladeta Jovovic, Sep 18 2004
G.f.: 32*x^5/(sqrt((1+x)*(1-3*x))*(1-x-sqrt((1+x)*(1-3*x)))^5). - Vladeta Jovovic, Sep 18 2004
a(n) = A111808(n,n-5). - Reinhard Zumkeller, Aug 17 2005
Assuming offset 0: a(n) = GegenbauerC(n,-n-5,-1/2) and a(n) = binomial(10+2*n,n)* hypergeom([-n, -n-10], [-9/2-n], 1/4). - Peter Luschny, May 09 2016
a(n) ~ 3^(n + 1/2) / (2*sqrt(Pi*n)). - Vaclav Kotesovec, Nov 09 2021