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 A381986 #19 Mar 14 2025 09:00:36
%S A381986 1,2,17,388,14329,727206,46984729,3689119624,341097752657,
%T A381986 36302764864330,4371463743828481,587606216836328460,
%U A381986 87219196719691250185,14168990447072685567214,2500554381188629649979593,476391652257266128440376336,97447147561230881896398507553
%N A381986 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 A381986 Let F(x) be the e.g.f. of A382000. F(x) = B(x*A(x)^2) = exp( 1/3 * Sum_{k>=1} binomial(3*k,k) * (x*A(x)^2)^k/k ).
%F A381986 a(n) = n! * Sum_{k=0..n} (2*k+1)^(n-k) * A002294(k)/(n-k)!.
%o A381986 (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(n-k)*binomial(5*k+1, k)/((5*k+1)*(n-k)!));
%Y A381986 Cf. A381984, A381985.
%Y A381986 Cf. A001764, A002294, A382000.
%K A381986 nonn
%O A381986 0,2
%A A381986 _Seiichi Manyama_, Mar 11 2025