A103872 a(n) = 3*trinomial(n+1,0) - trinomial(n+2,0).

0, 2, 2, 6, 12, 30, 72, 182, 464, 1206, 3170, 8426, 22596, 61074, 166194, 454950, 1251984, 3461574, 9611190, 26787378, 74916660, 210178458, 591347988, 1668172842, 4717282752, 13369522250, 37970114702, 108045430902

Offset: 0

Author

Eric W. Weisstein, Feb 19 2005

Keywords

• nonn
• easy

Comments

First differs from A059727 for n = 8.

Essentially twice A005043.

Links

• Eric Weisstein's World of Mathematics, Trinomial Coefficient

Crossrefs

Cf. A005043, A059727.

Programs

Maple

trinomial := n -> simplify(GegenbauerC(n,-n,-1/2)):
a := n -> 3*trinomial(n+1) - trinomial(n+2):
seq(a(n), n=0..27); # Peter Luschny, May 07 2016

Mathematica

Table[(4*2^n (2n + 3)!! (3 Hypergeometric2F1[-2 - n, -1 - n, -3/2 - n, 1/4] - 4 Hypergeometric2F1[-2 - n, -2 - n, -3/2 - n, 1/4]))/(n + 2)!, {n, 0, 20}] (* Vladimir Reshetnikov, May 07 2016 *)