A378883 G.f. A(x) satisfies A(x) = 1 + x*A(x)^3/(1 - x*A(x)^5).

1, 1, 4, 24, 171, 1338, 11109, 96100, 856762, 7816616, 72627241, 684859147, 6537520290, 63050669143, 613441446154, 6013687144000, 59343220508344, 589004488233064, 5876204912724812, 58893312496308755, 592682966496901253, 5986771171677305889, 60677419447552591497

Offset

0,3

Links

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

Formula

G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^2/(1 - x*A(x)^5)).

If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

G.f.: 1 + Series_Reversion( x / ((1+x)^3 * (1+x*(1+x)^2)) ). - Seiichi Manyama, Oct 07 2025

Prog

(PARI) a(n, r=1, s=1, t=3, u=5) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A271469, A378882.

Sequence in context: A369478 A368975 A366980 * A369471 A347651 A032349

Adjacent sequences: A378880 A378881 A378882 * A378884 A378885 A378886

Keyword

nonn

Author

Seiichi Manyama, Dec 09 2024

Status

approved