A365155 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^2 )^2.

1, 2, 13, 98, 838, 7690, 74047, 738028, 7549658, 78811732, 836219773, 8991739874, 97769604542, 1073156173442, 11875174074608, 132333387616600, 1483789788291516, 16727705523572128, 189496296040063170, 2155984626357225948, 24625450759174328948

Offset

0,2

Links

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

Formula

If g.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(s*k,n-k)/(n+k+1).

Prog

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

Crossrefs

Cf. A214372, A365156.

Sequence in context: A300633 A340451 A064325 * A123619 A341954 A187746

Adjacent sequences: A365152 A365153 A365154 * A365156 A365157 A365158

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved