A369621 Expansion of (1/x) * Series_Reversion( x / (1/(1-x) + x^3) ).

1, 1, 2, 6, 18, 57, 191, 660, 2334, 8417, 30831, 114380, 428915, 1623143, 6190876, 23774613, 91849846, 356735941, 1392091107, 5455425618, 21460947111, 84717452192, 335479515201, 1332327233554, 5305235886691, 21176621863427, 84720103674498

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/3)} binomial(n+1,k) * binomial(2*n-4*k,n-3*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)+x^3))/x)
(PARI) a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(2*n-4*k, n-3*k))/(n+1);

Crossrefs

Cf. A369622, A369623.

Sequence in context: A307496 A339044 A125305 * A273203 A148458 A148459

Adjacent sequences: A369618 A369619 A369620 * A369622 A369623 A369624

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2024

Status

approved