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 A382030 #19 Mar 14 2025 04:45:15
%S A382030 1,1,3,37,817,25741,1053211,52957297,3157457185,217695187801,
%T A382030 17036331544531,1491702434847901,144479729938558609,
%U A382030 15335923797225215653,1770255543485671432555,220776904683577075549801,29582947262972619472787521,4238424613351537181204589745,646565304924896452410832170787
%N A382030 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 A382030 Let F(x) be the e.g.f. of A382043. F(x) = log(A(x))/x = B(x*A(x)^2).
%F A382030 a(n) = n! * Sum_{k=0..n-1} (2*k+1)^(n-k-1) * binomial(n+2*k,k)/((n+2*k) * (n-k-1)!) for n > 0.
%o A382030 (PARI) a(n) = if(n==0, 1, n!*sum(k=0, n-1, (2*k+1)^(n-k-1)*binomial(n+2*k, k)/((n+2*k)*(n-k-1)!)));
%Y A382030 Cf. A212722, A382029, A382031.
%Y A382030 Cf. A001764, A382043.
%K A382030 nonn
%O A382030 0,3
%A A382030 _Seiichi Manyama_, Mar 12 2025