A368976 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^3)^2 ).

1, 4, 26, 202, 1729, 15730, 149249, 1460300, 14627340, 149254996, 1545959720, 16212144520, 171789072036, 1836515799464, 19783708310984, 214539449634588, 2340148164406642, 25658221358522584, 282627226176802000, 3126081536554547488, 34706443838025828198

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..932

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+k+1,k) * binomial(5*n-2*k+3,n-3*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x+x^3)^2)/x)
(PARI) a(n, s=3, 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);

Crossrefs

Cf. A368970, A368974.

Cf. A368968.

Sequence in context: A271935 A246509 A369107 * A253255 A141381 A369124

Adjacent sequences: A368973 A368974 A368975 * A368977 A368978 A368979

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2024

Status

approved