A382044 - OEIS

%I #10 Mar 13 2025 09:52:07

%S 1,1,12,252,8096,352120,19372512,1290832480,101078857728,

%T 9098805892608,925857411706880,105098610198360064,

%U 13167689873652178944,1804954814456584081408,268702350796640969736192,43172786067215188056023040,7446421094705349321120677888,1372319952106065844255081037824

%N E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^4*exp(2*x*A(x)).

%F a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * binomial(n+3*k+1,k)/((n+3*k+1) * (n-k)!).

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

%Y Cf. A366232, A379690, A382043.

%Y Cf. A365175, A382031.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 13 2025