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 A382033 #18 Mar 14 2025 09:00:17
%S A382033 1,1,7,109,2653,88261,3731581,191571493,11576241769,804996352873,
%T A382033 63324553740121,5559962513556001,539015912053933645,
%U A382033 57188111522488589293,6591136171961660099509,820029701725988751533341,109537705061927547203868241,15635869913619342121140932689
%N A382033 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))^3), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.
%F A382033 a(n) = (n-1)! * Sum_{k=0..n-1} (k+1)^(n-k-1) * binomial(3*n,k)/(n-k-1)! for n > 0.
%F A382033 Let F(x) be the e.g.f. of A377554. F(x) = log(A(x))/x = B(x*A(x))^3.
%F A382033 E.g.f.: A(x) = exp( Series_Reversion( x/(1 + x*exp(x))^3 ) ).
%o A382033 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(3*n, k)/(n-k-1)!));
%Y A382033 Cf. A161630, A382032, A382034.
%Y A382033 Cf. A001764, A377554.
%K A382033 nonn
%O A382033 0,3
%A A382033 _Seiichi Manyama_, Mar 12 2025