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 A376474 #12 Sep 24 2024 15:35:21
%S A376474 1,0,2,6,84,840,14160,246960,5438160,132209280,3696265440,
%T A376474 114042297600,3898083752640,145315002792960,5886559994515200,
%U A376474 257081021880883200,12051082491262214400,603307920100773888000,32132914081702520486400,1814085935013542141952000,108218538908648830498636800
%N A376474 E.g.f. satisfies A(x) = exp( x^2*A(x)^2 / (1 - x*A(x)) ).
%H A376474 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A376474 E.g.f.: (1/x) * Series_Reversion( x*exp(-x^2 / (1 - x)) ).
%F A376474 a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(k-1) * binomial(n-k-1,n-2*k)/k!.
%F A376474 a(n) ~ s^2 * (2-r*s) * n^(n-1) / (sqrt(2 - 2*r*s + 4*r^2*s^2 - 4*r^3*s^3 + r^4*s^4) * r^(n-1) * exp(n)), where r = exp(1 - sqrt(7/3) * cos(arctan(3^(-3/2))/3) + sqrt(7) * sin(arctan(3^(-3/2))/3)) * ((1 + sqrt(7) * cos(arctan(3^(3/2))/3) - sqrt(21) * sin(arctan(3^(3/2))/3))/3) = 0.311460490854501594554904428274272083649... and s = exp(-1 + sqrt(7/3) * cos(arctan(3^(-3/2))/3) - sqrt(7) * sin(arctan(3^(-3/2))/3)) = 1.428887069084244135127491236860585605773... - _Vaclav Kotesovec_, Sep 24 2024
%o A376474 (PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*binomial(n-k-1, n-2*k)/k!);
%Y A376474 Cf. A052873, A376475.
%Y A376474 Cf. A052845.
%K A376474 nonn
%O A376474 0,3
%A A376474 _Seiichi Manyama_, Sep 24 2024