A364986 - OEIS

%I #12 Aug 15 2023 11:58:13

%S 1,1,8,129,3196,107465,4575966,236120059,14322901832,998966928897,

%T 78770826493210,6929685905371691,672900446143476156,

%U 71491442785783506577,8249400210035835040022,1027394346436911560475915,137360293432089585554830096

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

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

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

%Y Cf. A364983, A364984, A364985.

%Y Cf. A161633, A364982, A364989.

%Y Cf. A002293.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 15 2023