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

5,2

Links

G. C. Greubel, Table of n, a(n) for n = 5..1005

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

Cf. A002426, A005717, A014531, A014532, A014533.

Sequence in context: A263942 A326138 A326131 * A253068 A055220 A027106

Adjacent sequences: A098467 A098468 A098469 * A098471 A098472 A098473

Keyword

nonn

Author

Eric W. Weisstein, Sep 09 2004

Status

approved