A369124 Expansion of (1/x) * Series_Reversion( x * ((1-x)^4+x^4) ).

1, 4, 26, 204, 1770, 16352, 157696, 1569096, 15988652, 165998624, 1749696208, 18673883696, 201394693864, 2191421381632, 24028822589440, 265238416143584, 2944999336948944, 32869042668479424, 368551132961138784, 4149643380825661824, 46897527236429235520

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

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

Prog

(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, (-1)^k*binomial(n+k, k)*binomial(5*n+3, n-4*k))/(n+1);

Crossrefs

Cf. A097188, A369123, A369125.

Cf. A369102.

Sequence in context: A368976 A253255 A141381 * A118971 A369102 A124554

Adjacent sequences: A369121 A369122 A369123 * A369125 A369126 A369127

Keyword

nonn

Author

Seiichi Manyama, Jan 13 2024

Status

approved