A360266 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(2*(n-2*k),n-2*k).

1, 2, 6, 22, 82, 312, 1210, 4752, 18834, 75184, 301856, 1217604, 4930626, 20032052, 81615072, 333328532, 1364264250, 5594210292, 22977466864, 94517423444, 389316529512, 1605533230256, 6628467569292, 27393187077144, 113310732332274, 469101108803052

Offset: 0

Author

Seiichi Manyama, Jan 31 2023

Keywords

• nonn

Comments

Diagonal of rational function 1/(1 - (x + y + x^3*y^2)). - Seiichi Manyama, Mar 23 2023

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006139, A360267.

Cf. A157004, A374598.

Programs

PARI

a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(2*(n-2*k), n-2*k));

PARI

my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1+x^2)))

Formula

G.f.: 1/sqrt(1 - 4*x*(1 + x^2)).

n*a(n) = 2*(2*n-1)*a(n-1) + 2*(2*n-3)*a(n-3).