A365122 G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^3)^3.

1, 3, 12, 64, 372, 2319, 15105, 101649, 701073, 4929657, 35207220, 254690517, 1862325262, 13742311074, 102204992352, 765328009950, 5765316776550, 43661497944861, 332217854059362, 2538540859615095, 19471592691620310, 149871698475060433, 1157188723053901449

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).

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A371616. - Seiichi Manyama, Dec 06 2024

Prog

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

Crossrefs

Cf. A006013, A365113.

Cf. A365119, A365121.

Cf. A371616.

Sequence in context: A203508 A052757 A345883 * A233397 A206226 A371495

Adjacent sequences: A365119 A365120 A365121 * A365123 A365124 A365125

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2023

Status

approved