A370781 Expansion of 1 / ( (1 - x)*(1 + 2*x)*(1 - 4*x) )^(1/3).

1, 1, 4, 10, 37, 121, 442, 1576, 5818, 21466, 80272, 301324, 1138762, 4320226, 16459132, 62904664, 241134553, 926678569, 3569385772, 13776307714, 53267766997, 206304355225, 800203300354, 3108008802064, 12086612436376, 47056902019336, 183400211694496

Offset: 0

Author

Seiichi Manyama, Mar 01 2024

Keywords

• nonn

Crossrefs

Cf. A004987, A370145.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/((1-x)*(1+2*x)*(1-4*x))^(1/3))

PARI

a(n) = sum(k=0, n\2, (-9)^k*binomial(-1/3, k)*binomial(n, 2*k)); \\ Seiichi Manyama, Aug 18 2025

Formula

a(n) ~ 2^(2*n+1) / (Gamma(1/3) * 3^(2/3) * n^(2/3)). - Vaclav Kotesovec, Mar 10 2024

a(n) = Sum_{k=0..floor(n/2)} A004987(k) * binomial(n,2*k). - Seiichi Manyama, Aug 18 2025