A367239 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^2)^3.

1, 1, 4, 19, 104, 615, 3829, 24728, 164122, 1112641, 7671781, 53634389, 379305155, 2708686547, 19505022538, 141470864166, 1032587621470, 7578835132264, 55901583657799, 414157062713599, 3080581445049863, 22996511364853472, 172230640045929990

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

Prog

(PARI) a(n, s=3, t=1, 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, A367240, A367241.

Sequence in context: A178302 A292098 A186997 * A062265 A088129 A369109

Adjacent sequences: A367236 A367237 A367238 * A367240 A367241 A367242

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved