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 A382037 #19 Mar 15 2025 09:42:27
%S A382037 1,1,9,160,4325,157896,7280077,406085632,26599741065,2001864880000,
%T A382037 170236619802161,16144762562002944,1689534516295056301,
%U A382037 193403842876754728960,24040636567791329323125,3224829927677539092791296,464325325579881390473331473,71428455280041816247241637888
%N A382037 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^3) ), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.
%F A382037 E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^3).
%F A382037 a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(3*n,k)/(n-k-1)! for n > 0.
%F A382037 E.g.f.: exp( Series_Reversion( x*exp(-x)/(1+x)^3 ) ).
%o A382037 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(3*n, k)/(n-k-1)!));
%Y A382037 Cf. A052873, A382036, A382038.
%Y A382037 Cf. A001764, A377830, A382033.
%K A382037 nonn
%O A382037 0,3
%A A382037 _Seiichi Manyama_, Mar 12 2025