A382885 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x) * A(x) )^3.

1, 3, 18, 121, 900, 7110, 58598, 498153, 4336533, 38463732, 346368351, 3158325168, 29102914959, 270582713670, 2535191045652, 23913087584045, 226892934532149, 2164080724942155, 20737076963936828, 199542537271568802, 1927347504059464995, 18679645863925666721

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f. A(x) satisfies A(x) = ( 1 + x * (1+x) * A(x)^(4/3) )^3.

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

G.f.: B(x)^3, where B(x) is the g.f. of A365178.

Prog

(PARI) a(n, r=3, s=1, t=4, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A052709, A371576.

Cf. A365178, A371483.

Sequence in context: A118348 A011792 A295537 * A183145 A127188 A355048

Adjacent sequences: A382882 A382883 A382884 * A382886 A382887 A382888

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2025

Status

approved