A385475 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^3 / (1+x)^4 ).

1, 10, 154, 2836, 57601, 1244584, 28063288, 652821724, 15551944804, 377503375150, 9303441938506, 232168129150420, 5854967533764766, 148981015820615968, 3820184959840942564, 98616983735455104412, 2560818171703792341484, 66845502538144505160040

Offset: 0

Author

Seiichi Manyama, Aug 01 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A064063, A385474.

Cf. A386723.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^3/(1+x)^4)/x)

PARI

a(n) = sum(k=0, n, 2^(n-k)*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 2^(n-k) * binomial(4*(n+1),k) * binomial(4*n-k+2,n-k).

a(n) = (1/(n+1)) * [x^n] ( (1+x)^4 / (1-2*x)^3 )^(n+1).