A367283 G.f. satisfies A(x) = 1 + x*A(x)^2 * (1 + x*A(x)^3)^2.

1, 1, 4, 20, 116, 728, 4818, 33100, 233824, 1687764, 12393520, 92291681, 695325926, 5290359124, 40591599128, 313725215636, 2440203573816, 19087022233906, 150042056387660, 1184734863936672, 9392213303130904, 74728563957003952, 596531545003840160

Offset: 0

Author

Seiichi Manyama, Nov 12 2023

Keywords

• nonn

Crossrefs

Cf. A002293, A073155, A214372, A367282.

Cf. A001764, A137952.

Programs

PARI

a(n, s=2, t=2, 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));

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).