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 A381989 #17 Mar 14 2025 09:00:39
%S A381989 1,2,19,514,22621,1369546,105616639,9901346554,1093292035609,
%T A381989 138977379784882,19990424969236171,3209995501651871890,
%U A381989 569216406245186726965,110476637766622355475898,23294266811686640511534199,5302371488162151660366545866,1295920217231693678343467474353
%N A381989 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 A381989 Let F(x) be the e.g.f. of A382001. F(x) = B(x*A(x)^2) = exp( 1/4 * Sum_{k>=1} binomial(4*k,k) * (x*A(x)^2)^k/k ).
%F A381989 a(n) = n! * Sum_{k=0..n} (2*k+1)^(n-k) * A002295(k)/(n-k)!.
%o A381989 (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(n-k)*binomial(6*k+1, k)/((6*k+1)*(n-k)!));
%Y A381989 Cf. A381987, A381988.
%Y A381989 Cf. A002293, A002295, A382001.
%K A381989 nonn
%O A381989 0,2
%A A381989 _Seiichi Manyama_, Mar 12 2025