A380605 Expansion of e.g.f. exp(2*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.

1, 2, 16, 260, 6544, 224672, 9797824, 518778752, 32332764160, 2319086302208, 188178044545024, 17043816700333568, 1704575787500099584, 186577340672207974400, 22185432394552519868416, 2847773562263558405439488, 392481896442656581445287936, 57805399208817471918851883008

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380515.

a(n) = 3 * n! * Sum_{k=0..n-1} 2^(n-k) * binomial(3*n+k,k)/((3*n+k) * (n-k-1)!) for n > 0.

Prog

(PARI) a(n) = if(n==0, 1, 3*n!*sum(k=0, n-1, 2^(n-k)*binomial(3*n+k, k)/((3*n+k)*(n-k-1)!)));

Crossrefs

Cf. A002293, A251574, A380515, A380606.

Sequence in context: A358145 A246739 A304317 * A351918 A326272 A372513

Adjacent sequences: A380602 A380603 A380604 * A380606 A380607 A380608

Keyword

nonn

Author

Seiichi Manyama, Jan 28 2025

Status

approved