A365123 G.f. satisfies A(x) = (1 + x / (1 - x*A(x))^4)^2.

1, 2, 9, 44, 244, 1438, 8858, 56340, 367160, 2438934, 16453015, 112411836, 776258588, 5409237100, 37988571802, 268606426836, 1910584687932, 13661702623498, 98148312810335, 708092115326436, 5127976641997944, 37264674894021280, 271650189521574734

Offset

0,2

Links

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

Formula

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

Prog

(PARI) a(n, s=4, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Crossrefs

Cf. A006632, A365114, A365124.

Sequence in context: A365129 A371576 A246812 * A108308 A119855 A047119

Adjacent sequences: A365120 A365121 A365122 * A365124 A365125 A365126

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2023

Status

approved