A380051 - OEIS

%I #7 Jan 11 2025 10:26:28

%S 1,1,2,1,-12,-15,526,1617,-49608,-302111,8126010,85724001,-2020009628,

%T -34232466255,696686324166,18267485751985,-310973114236944,

%U -12533263924965183,168118610439268594,10727427541319225793,-100693940482485604260,-11178369799980253348079

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

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

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

%Y Cf. A006153, A380050.

%Y Cf. A380047.

%K sign

%O 0,3

%A _Seiichi Manyama_, Jan 11 2025