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 A382089 #9 Mar 15 2025 10:14:27
%S A382089 1,1,11,268,10301,543576,36542527,2987431168,287751180537,
%T A382089 31916479461760,4006558784401811,561568192339405824,
%U A382089 86932015931716588789,14730649112418719484928,2711977587454133506904775,539042371050858695696121856,115046065096051639979478349553
%N A382089 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^4) ), where B(x) = 1 + x*B(x)^5 is the g.f. of A002294.
%F A382089 E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^4).
%F A382089 a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(4*n+k-1,k)/(n-k-1)! for n > 0.
%F A382089 E.g.f.: exp( Series_Reversion( x * (1-x)^4 * exp(-x) ) ).
%o A382089 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(4*n+k-1, k)/(n-k-1)!));
%Y A382089 Cf. A382086, A382087, A382088.
%Y A382089 Cf. A002294.
%K A382089 nonn
%O A382089 0,3
%A A382089 _Seiichi Manyama_, Mar 15 2025