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 A381997 #15 Mar 22 2025 10:49:47
%S A381997 1,1,12,240,7328,303400,15904032,1010252320,75442821120,6478112692224,
%T A381997 628915387166720,68121797696449024,8144844724723482624,
%U A381997 1065508614975814537216,151392999512027274215424,23217165210450099377479680,3822334349865128121165283328,672407573328393115218009063424
%N A381997 E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^4.
%F A381997 a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A002293(k)/(n-k)!.
%F A381997 a(n) ~ 2^(n+1) * n^(n-1) * sqrt(1 + LambertW(27/128)) / (3^(3/2) * exp(n) * LambertW(27/128)^n). - _Vaclav Kotesovec_, Mar 22 2025
%p A381997 A381997 := proc(n)
%p A381997 n!*add((2*k)^(n-k)*binomial(4*k+1,k)/(4*k+1)/(n-k)!,k=0..n) ;
%p A381997 end proc:
%p A381997 seq(A381997(n),n=0..60) ; # _R. J. Mathar_, Mar 12 2025
%o A381997 (PARI) a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(4*k+1, k)/((4*k+1)*(n-k)!));
%Y A381997 Cf. A336950, A381998, A381999, A382000, A382001.
%Y A381997 Cf. A002293, A364987, A381983.
%K A381997 nonn
%O A381997 0,3
%A A381997 _Seiichi Manyama_, Mar 12 2025