A369489 Expansion of (1/x) * Series_Reversion( x / (1-x) * (1-x-x^3)^2 ).

1, 1, 2, 7, 26, 98, 387, 1589, 6688, 28676, 124880, 550926, 2456831, 11056693, 50152457, 229050621, 1052393802, 4861062466, 22559964766, 105144660498, 491922058878, 2309456782464, 10876596029574, 51372213424194, 243283513468707, 1154929327702775, 5495105429597720

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1-x)*(1-x-x^3)^2)/x)
(PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t-u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A368962, A368966, A368968, A369011.

Cf. A054514, A369486.

Sequence in context: A113436 A126223 A369231 * A273320 A114121 A049775

Adjacent sequences: A369486 A369487 A369488 * A369490 A369491 A369492

Keyword

nonn

Author

Seiichi Manyama, Jan 24 2024

Status

approved