A369484 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^3)^2) ).

1, 3, 12, 57, 301, 1700, 10045, 61303, 383335, 2443113, 15811317, 103627692, 686402602, 4587643765, 30900426417, 209539509967, 1429344492215, 9801262309209, 67523359213569, 467136798336153, 3243948604314619, 22604271635042853, 158001453530915361

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(2*n+2,k) * binomial(3*n-k+3,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)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);

Crossrefs

Cf. A369483, A369485.

Sequence in context: A166991 A276366 A243521 * A151498 A103370 A094149

Adjacent sequences: A369481 A369482 A369483 * A369485 A369486 A369487

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved