This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380096 #12 Jan 12 2025 07:56:19
%S A380096 1,1,12,289,10724,540745,34551886,2676439507,243782162408,
%T A380096 25535467766593,3024360522754010,399665508962874451,
%U A380096 58301379215119084012,9305724270031402836337,1613262216112899513140630,301870732625016111841693795,60639884085040694650040518736
%N A380096 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*A(x)^3*exp(x*A(x)^3) )^(1/3).
%F A380096 E.g.f.: ( (1/x) * Series_Reversion(x*(1 - 3*x*exp(x))) )^(1/3).
%F A380096 a(n) = n! * Sum_{k=0..n} 3^k * k^(n-k) * binomial(n+k+1/3,k)/( (3*n+3*k+1)*(n-k)! ).
%F A380096 a(n) = (n!/(3*n+1)) * Sum_{k=0..n} (-3)^k * k^(n-k) * binomial(-n-1/3,k)/(n-k)!.
%o A380096 (PARI) a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(n+k+1/3, k)/((3*n+3*k+1)*(n-k)!));
%Y A380096 Cf. A213644, A380095.
%Y A380096 Cf. A380043, A380097.
%K A380096 nonn
%O A380096 0,3
%A A380096 _Seiichi Manyama_, Jan 12 2025