A367284 G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^3)^3.

1, 1, 4, 19, 107, 648, 4144, 27500, 187654, 1308361, 9280049, 66749995, 485741501, 3569653591, 26454406231, 197482954338, 1483619134872, 11208536870979, 85101381927454, 649017399223259, 4969510058193925, 38189305411228229, 294440263583908772

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A002293, A099234, A364742, A367261.

Sequence in context: A348802 A379513 A052751 * A249934 A174992 A182541

Adjacent sequences: A367281 A367282 A367283 * A367285 A367286 A367287

Keyword

nonn

Author

Seiichi Manyama, Nov 12 2023

Status

approved