A365158 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^3 )^3.

1, 3, 30, 352, 4680, 66852, 1002420, 15562917, 248028012, 4034367018, 66704722941, 1117794312987, 18942067925094, 324048616144950, 5588890522700901, 97074537335184054, 1696556614819124517, 29812650855663860436, 526429300730659123740

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Crossrefs

Cf. A361305, A365157.

Sequence in context: A160473 A144283 A229299 * A178016 A365152 A372087

Adjacent sequences: A365155 A365156 A365157 * A365159 A365160 A365161

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved