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 A382088 #11 Mar 15 2025 10:13:27
%S A382088 1,1,9,178,5549,237456,12945037,858203872,67035559257,6029839290880,
%T A382088 613862192499281,69777500840918784,8760124051527691141,
%U A382088 1203852634738613966848,179746834136205848167125,28975042890917781500747776,5015346425440407318539964593,927775677566572703009955053568
%N A382088 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^3) ), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
%F A382088 E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^3).
%F A382088 a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(3*n+k-1,k)/(n-k-1)! for n > 0.
%F A382088 E.g.f.: exp( Series_Reversion( x * (1-x)^3 * exp(-x) ) ).
%o A382088 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(3*n+k-1, k)/(n-k-1)!));
%Y A382088 Cf. A382086, A382087, A382089.
%Y A382088 Cf. A002293, A377833, A382038.
%K A382088 nonn
%O A382088 0,3
%A A382088 _Seiichi Manyama_, Mar 15 2025