A369230 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^3 ).

1, 0, 3, 3, 24, 54, 283, 900, 4098, 15286, 66555, 268173, 1156951, 4852722, 21007605, 90167059, 393152058, 1712432070, 7524092134, 33112353060, 146518404963, 649861681966, 2893369443183, 12913307575722, 57800647230933, 259298148600504, 1165967972216967

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^2)^3)/x)
(PARI) a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A366049, A369229.

Cf. A369078.

Sequence in context: A255355 A201133 A036114 * A219909 A092864 A183894

Adjacent sequences: A369227 A369228 A369229 * A369231 A369232 A369233

Keyword

nonn

Author

Seiichi Manyama, Jan 17 2024

Status

approved