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 A382058 #15 Mar 14 2025 09:00:26
%S A382058 1,1,5,67,1465,44541,1735681,82527439,4632741905,299875704697,
%T A382058 21989097804961,1801520077445331,163092373817762137,
%U A382058 16168084561101716725,1741946677697976052577,202668693570279026375671,25324088113475137179021601,3382305512670022948599733233,480858973986045019386825360577
%N A382058 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))^2), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.
%F A382058 Let F(x) be the e.g.f. of A377546. F(x) = log(A(x))/x = B(x*A(x))^2.
%F A382058 E.g.f.: A(x) = exp( Series_Reversion( x*(1 - x*exp(x))^2 ) ).
%F A382058 a(n) = 2 * n! * Sum_{k=0..n-1} (k+1)^(n-k-1) * binomial(2*n+k,k)/((2*n+k) * (n-k-1)!) for n > 0.
%o A382058 (PARI) a(n) = if(n==0, 1, 2*n!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(2*n+k, k)/((2*n+k)*(n-k-1)!)));
%Y A382058 Cf. A161629, A382059.
%Y A382058 Cf. A161635, A382032.
%Y A382058 Cf. A001764, A377546, A382033.
%K A382058 nonn
%O A382058 0,3
%A A382058 _Seiichi Manyama_, Mar 13 2025