A369631 Expansion of (1/x) * Series_Reversion( x * (1/(1+x^4) - x) ).

1, 1, 2, 5, 15, 49, 168, 594, 2149, 7920, 29640, 112359, 430564, 1665197, 6491280, 25478886, 100611695, 399421439, 1593221090, 6382176160, 25664184349, 103560846454, 419215870860, 1701907025715, 6927658961599, 28268225980197, 115608889788304

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/4)} binomial(2*n-4*k+1,k) * binomial(2*n-4*k,n-4*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x^4)-x))/x)
(PARI) a(n) = sum(k=0, n\4, binomial(2*n-4*k+1, k)*binomial(2*n-4*k, n-4*k))/(n+1);

Crossrefs

Cf. A007863, A199874, A369630.

Cf. A227035.

Sequence in context: A149936 A189176 A366054 * A063021 A364833 A301832

Adjacent sequences: A369628 A369629 A369630 * A369632 A369633 A369634

Keyword

nonn

Author

Seiichi Manyama, Jan 28 2024

Status

approved