A357089 - OEIS

%I #8 Sep 11 2022 10:07:18

%S 1,0,0,1,6,25,140,1561,19586,228425,2870160,44172601,780614846,

%T 14499946825,284310704860,6089231941521,142225796401786,

%U 3537029819020905,92766573133851240,2577870903366020521,75999605064376599606,2362944241092314079145

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

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

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

%Y Cf. A349588, A357088.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 11 2022