A369600 Expansion of (1/x) * Series_Reversion( x * (1/(1+x)^3 - x^3) ).

1, 3, 12, 56, 291, 1638, 9780, 60948, 391821, 2577575, 17256918, 117150228, 804343302, 5575177026, 38957753136, 274143594685, 1941037464402, 13818185220783, 98848503602394, 710185896393792, 5122358166219855, 37076879861508830, 269235792063692580

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for reversions of series

Formula

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

Prog

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

Crossrefs

Cf. A198888, A369599.

Cf. A274379, A274735.

Sequence in context: A284712 A284713 A180256 * A027390 A349513 A009499

Adjacent sequences: A369597 A369598 A369599 * A369601 A369602 A369603

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2024

Status

approved