A368975 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^2)^2 ).

1, 4, 24, 170, 1320, 10868, 93199, 823548, 7446480, 68567202, 640757920, 6061477500, 57933260067, 558580920160, 5426644737984, 53069206438226, 522004849765080, 5161083186971000, 51262685633583970, 511272660117154692, 5118240198221249088

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..973
• Index entries for reversions of series

Crossrefs

Cf. A368969, A368973.

Cf. A368967.

Programs

PARI

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

PARI

a(n, s=2, t=2, u=2) = sum(k=0, n\s, (-1)^k*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/2)} (-1)^k * binomial(2*n+k+1,k) * binomial(5*n-k+3,n-2*k).