A369262 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^2)^3 ).

1, 1, 5, 17, 80, 363, 1792, 8969, 46319, 242994, 1296046, 6996163, 38175142, 210162728, 1166020560, 6512854409, 36593709385, 206686641555, 1172856064443, 6683348391034, 38228129813288, 219411037878578, 1263245957786120, 7293833100110787, 42224142505632305

Offset

0,3

Links

Table of n, a(n) for n=0..24.

P. Bala, Fractional iteration of a series inversion operator

Index entries for reversions of series

Formula

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

a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^2)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024

Prog

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

Crossrefs

Cf. A052709, A369226.

Cf. A369263, A369264.

Sequence in context: A149748 A151494 A307052 * A053418 A151882 A359206

Adjacent sequences: A369259 A369260 A369261 * A369263 A369264 A369265

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2024

Status

approved