A382016 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.

1, 1, 3, 37, 901, 32141, 1502701, 86737645, 5952271977, 473117681881, 42731313784921, 4321503662185601, 483709266378568429, 59360036142346311685, 7924411424305558028757, 1143251381667547987358581, 177245340974472998607370321, 29386977237154379581209716657

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A161629, A161630, A382015.

Cf. A002293, A380513.

Sequence in context: A143412 A382030 A331656 * A003717 A354020 A201697

Adjacent sequences: A382000 A382001 A382015 * A382029 A382030 A382031

Keyword

nonn,new

Author

Seiichi Manyama, Mar 12 2025

Status

approved