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 A362281 #21 Feb 16 2025 08:34:05
%S A362281 1,1,5,19,241,1601,32581,308995,8655809,106673761,3805452901,
%T A362281 57704760851,2500580809585,45018720191329,2295683481085541,
%U A362281 47848514992963651,2806491306922172161,66464103165835330625,4407449313521981148229,116893033842508769526931
%N A362281 a(n) = n! * Sum_{k=0..floor(n/2)} n^k * binomial(n-k,k)/(n-k)!.
%H A362281 Seiichi Manyama, <a href="/A362281/b362281.txt">Table of n, a(n) for n = 0..395</a>
%H A362281 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362281 a(n) = n! * [x^n] exp(x + n*x^2).
%F A362281 E.g.f.: exp( sqrt( -LambertW(-2*x^2)/2 ) ) / (1 + LambertW(-2*x^2)).
%F A362281 a(n) ~ (1 + (-1)^n/exp(sqrt(2))) * 2^((n-1)/2) * n^n / exp(n/2 - 1/sqrt(2)). - _Vaclav Kotesovec_, Apr 15 2023
%o A362281 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(-lambertw(-2*x^2)/2))/(1+lambertw(-2*x^2))))
%Y A362281 Cf. A277614, A362282.
%K A362281 nonn
%O A362281 0,3
%A A362281 _Seiichi Manyama_, Apr 14 2023