A382893 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^2.

1, 2, 11, 60, 365, 2350, 15767, 109048, 771993, 5567066, 40751267, 302018484, 2261763205, 17088919814, 130108591407, 997225521136, 7688232599089, 59581977618098, 463890112373563, 3626778446099756, 28461425971969693, 224114796803735774, 1770236735807921863

Offset

0,2

Links

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

Formula

G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^2 * A(x)^(3/2) )^2.

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(s*k,n-k)/(t*k+u*(n-k)+r).

G.f.: B(x)^2, where B(x) is the g.f. of A366221.

Prog

(PARI) a(n, r=2, s=2, t=3, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A073155, A382886.

Cf. A366221.

Sequence in context: A251180 A286194 A164034 * A240548 A386019 A255549

Adjacent sequences: A382890 A382891 A382892 * A382894 A382895 A382896

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2025

Status

approved