A365136 G.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^3)^3.

1, 3, 21, 172, 1563, 15141, 153240, 1601160, 17140686, 187026210, 2072333697, 23255417925, 263757940688, 3018654757212, 34817822871933, 404324843585061, 4723248984803013, 55467143334798210, 654435356605769574, 7753961433310798095, 92220463998917459652

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A161797, A365135.

Cf. A365122.

Sequence in context: A206397 A392860 A247480 * A228923 A287995 A379086

Adjacent sequences: A365133 A365134 A365135 * A365137 A365138 A365139

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved