A378465 Expansion of (1/x) * Series_Reversion( x * (1 - x - x/(1 - x)) ).

1, 2, 9, 51, 324, 2206, 15737, 116098, 878495, 6780544, 53175176, 422508607, 3394004192, 27518168434, 224899980185, 1850830170355, 15324273361220, 127562500961502, 1066940307951747, 8962213871074848, 75572666059970392, 639485384767169924, 5428457500063304272

Offset

0,2

Links

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

Index entries for reversions of series

Formula

G.f.: exp( Sum_{k>=1} A378460(k) * x^k/k ).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x/(1 - x))^(n+1).

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

a(n) ~ ((16 + 12*2^(1/3) + 9*2^(2/3))/5)^n / (sqrt(6*(4 - 3*2^(1/3))*Pi) * n^(3/2)). - Vaclav Kotesovec, Nov 27 2024

Prog

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

Crossrefs

Cf. A151374, A378466.

Cf. A378460.

Sequence in context: A020087 A277378 A026945 * A374567 A246464 A355397

Adjacent sequences: A378462 A378463 A378464 * A378466 A378467 A378468

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2024

Status

approved