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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.
2
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
5,2
LINKS
Eric Weisstein's World of Mathematics, Trinomial Coefficient
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
MAPLE
# Assuming offset 0:
a := n -> simplify(GegenbauerC(n, -n-5, -1/2)):
seq(a(n), n=0..25); # Peter Luschny, May 09 2016
MATHEMATICA
Table[GegenbauerC[n, -n - 5, -1/2], {n, 0, 50}] (* G. C. Greubel, Feb 28 2017 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 09 2004
STATUS
approved