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 A376494 #15 Aug 05 2025 07:33:07
%S A376494 1,0,2,6,84,720,12000,178920,3744720,79531200,2056652640,56284351200,
%T A376494 1753673423040,58443081016320,2142625074670080,83948606126985600,
%U A376494 3549356731374854400,159643527455123712000,7656564912324122995200
%N A376494 E.g.f. satisfies A(x) = exp(x^2 * A(x)^2 / (1 - x)).
%H A376494 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376494 E.g.f.: exp( -LambertW(-2*x^2 / (1-x))/2 ).
%F A376494 a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * binomial(n-k-1,n-2*k)/k!.
%F A376494 a(n) ~ sqrt(16 + 2*exp(-1) - 2*exp(-1/2)*sqrt(exp(-1)+8)) * (exp(1/2)*sqrt(exp(-1)+8) - 1) * 2^(2*n-2) * n^(n-1) / ((4 + exp(-1) - exp(-1/2)*sqrt(exp(-1)+8)) * (sqrt(1 + 8*exp(1)) - 1)^n). - _Vaclav Kotesovec_, Aug 05 2025
%o A376494 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x^2/(1-x))/2)))
%o A376494 (PARI) a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(n-k-1, n-2*k)/k!);
%Y A376494 Cf. A052868, A376495.
%Y A376494 Cf. A052845, A376474.
%K A376494 nonn
%O A376494 0,3
%A A376494 _Seiichi Manyama_, Sep 25 2024