A357089 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3 / 6.

1, 0, 0, 1, 6, 25, 140, 1561, 19586, 228425, 2870160, 44172601, 780614846, 14499946825, 284310704860, 6089231941521, 142225796401786, 3537029819020905, 92766573133851240, 2577870903366020521, 75999605064376599606, 2362944241092314079145

Offset

0,5

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * Stirling2(n,3*k)/(6^k * k!).

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*stirling(n, 3*k, 2)/(6^k*k!));

Crossrefs

Cf. A349588, A357088.

Sequence in context: A136593 A012293 A012594 * A242858 A200375 A009464

Adjacent sequences: A357086 A357087 A357088 * A357090 A357091 A357092

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2022

Status

approved