A367241 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x)^2)^3.

1, 1, 6, 42, 335, 2886, 26166, 246028, 2377161, 23459250, 235452723, 2395998060, 24663705924, 256358715585, 2686893609015, 28364934291912, 301334854075058, 3219067773992448, 34558507062732315, 372646872976093760, 4034272938342360147

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).

Prog

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

Crossrefs

Cf. A001764, A367239, A367240.

Sequence in context: A082302 A144223 A320758 * A262671 A029588 A001725

Adjacent sequences: A367238 A367239 A367240 * A367242 A367243 A367244

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved