A365131 G.f. A(x) satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^3)^2.

1, 2, 11, 62, 395, 2662, 18720, 135738, 1007607, 7619456, 58488028, 454556544, 3569655975, 28282204680, 225796917864, 1814732935968, 14670580718486, 119215212413412, 973246346463636, 7978384233270126, 65649676250344747, 542031604244083664

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

From Seiichi Manyama, Oct 08 2025: (Start)

G.f.: (1/x) * Series_Reversion( x / (1 + x * (1 + x)^3)^2 ).

G.f.: B(x)^2, where B(x) is the g.f. of A367285. (End)

Prog

(PARI) a(n, s=3, t=2) = sum(k=0, n, binomial(t*(n+1), k)*binomial(s*k, n-k))/(n+1);

Crossrefs

Cf. A364742, A365132.

Cf. A137952, A367285.

Sequence in context: A162274 A183160 A020078 * A002629 A235937 A383564

Adjacent sequences: A365128 A365129 A365130 * A365132 A365133 A365134

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved