A368968 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^3)^2 ).

1, 4, 26, 206, 1813, 17030, 167229, 1695920, 17624932, 186722580, 2009077416, 21894695420, 241170873096, 2680761546396, 30032284769832, 338744791093796, 3843699928567438, 43844993166845920, 502497843180361288, 5783367971991398760, 66815895492710846218

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..917
• Index entries for reversions of series

Crossrefs

Cf. A368962, A368966, A369011.

Cf. A368967.

Programs

PARI

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

PARI

a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(5*n-2*k+3,n-3*k).