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 A382031 #20 Mar 14 2025 04:45:11
%S A382031 1,1,3,43,1177,46681,2419291,154587427,11735209585,1031418915121,
%T A382031 102979800567091,11510663862332251,1423811747933017609,
%U A382031 193073662118499898633,28479005472094048953355,4539456019668776334683731,777538096585429376795405281,142419954152382631361835929185
%N A382031 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x)^2)), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
%F A382031 Let F(x) be the e.g.f. of A382044. F(x) = log(A(x))/x = B(x*A(x)^2).
%F A382031 a(n) = n! * Sum_{k=0..n-1} (2*k+1)^(n-k-1) * binomial(n+3*k,k)/((n+3*k) * (n-k-1)!) for n > 0.
%o A382031 (PARI) a(n) = if(n==0, 1, n!*sum(k=0, n-1, (2*k+1)^(n-k-1)*binomial(n+3*k, k)/((n+3*k)*(n-k-1)!)));
%Y A382031 Cf. A212722, A382029, A382030.
%Y A382031 Cf. A380513, A382016.
%Y A382031 Cf. A002293, A382044.
%K A382031 nonn
%O A382031 0,3
%A A382031 _Seiichi Manyama_, Mar 12 2025