A369102 Expansion of (1/x) * Series_Reversion( x * ((1-x)^4-x^4) ).

1, 4, 26, 204, 1772, 16408, 158752, 1585968, 16235472, 169423232, 1795611168, 19275231872, 209140483328, 2289981517312, 25271472702464, 280795784911616, 3138701648319744, 35270318924758016, 398215386792574464, 4515067063939210240, 51388662166213954560

Offset: 0

Author

Seiichi Manyama, Jan 13 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A097188, A151374.

Cf. A063021.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(5*n+3, n-4*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(5*n+3,n-4*k).