A369229 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^2 ).

1, 1, 4, 15, 65, 298, 1429, 7073, 35869, 185403, 973198, 5173644, 27797914, 150715321, 823541564, 4530609391, 25073291597, 139492998775, 779706274423, 4376600956063, 24659875131049, 139424357994344, 790763858547445, 4497788153203946, 25650342635871106

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^2)^2)/x)
(PARI) a(n, s=2, t=2, 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, A369230.

Sequence in context: A349202 A318121 A357785 * A097422 A102129 A164310

Adjacent sequences: A369226 A369227 A369228 * A369230 A369231 A369232

Keyword

nonn

Author

Seiichi Manyama, Jan 17 2024

Status

approved