A365010 - OEIS

%I #14 Aug 16 2023 12:03:33

%S 1,1,4,39,596,12365,324714,10329655,386190328,16597810233,

%T 806356830230,43700423019011,2613919719004692,171053575111641157,

%U 12156558707970920866,932424974682447304815,76772968644326739801584,6754080601542663692950769

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

%F a(n) = n! * Sum_{k=0..n} (-k)^(n-k) * A001764(k)/(n-k)!.

%p A365010 := proc(n)

%p     add( (-k)^(n-k)*A001764(k)/(n-k)!,k=0..n) ;

%p     %*n! ;

%p end proc:

%p seq(A365010(n),n=0..80); # _R. J. Mathar_, Aug 16 2023

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

%Y Cf. A295239, A302397, A365011.

%Y Cf. A001764, A364983.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 15 2023