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 A382086 #10 Mar 15 2025 10:11:19
%S A382086 1,1,5,52,845,18816,533617,18404800,748039833,35016198400,
%T A382086 1855389108221,109781344134144,7174844881882405,513331696318615552,
%U A382086 39905830821183755625,3349445733955326754816,301886246619209909215793,29080090017105458412257280,2981488457660004727761477493
%N A382086 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * C(x)) ), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A382086 E.g.f. A(x) satisfies A(x) = exp(x*A(x) * C(x*A(x))).
%F A382086 a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(n+k-1,k)/(n-k-1)! for n > 0.
%F A382086 E.g.f.: exp( Series_Reversion( x * (1-x) * exp(-x) ) ).
%F A382086 a(n) ~ phi^(3*n - 3/2) * n^(n-1) / (5^(1/4) * exp((n - 1/phi)/phi)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Mar 15 2025
%o A382086 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(n+k-1, k)/(n-k-1)!));
%Y A382086 Cf. A382087, A382088, A382089.
%Y A382086 Cf. A000108, A377831, A382036.
%K A382086 nonn
%O A382086 0,3
%A A382086 _Seiichi Manyama_, Mar 15 2025