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 A290840 #28 Jul 20 2024 06:45:15
%S A290840 1,2,12,117,1584,27525,585108,14726411,428551616,14161828185,
%T A290840 523952280900,21456869976135,963553844335536,47078974421716757,
%U A290840 2486272976536821332,141118622400977894475,8566597074999702384384,553816179165426157329201,37985975117322654130568964
%N A290840 a(n) = n! * [x^n] exp(n*x)/(1 + LambertW(-x)).
%H A290840 G. C. Greubel, <a href="/A290840/b290840.txt">Table of n, a(n) for n = 0..365</a>
%H A290840 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A290840 Martin Svatoš, Peter Jung, Jan Tóth, Yuyi Wang, and Ondřej Kuželka, <a href="https://arxiv.org/abs/2302.04606">On Discovering Interesting Combinatorial Integer Sequences</a>, arXiv:2302.04606 [cs.LO], 2023, p. 17.
%F A290840 a(n) = A290824(n,n).
%F A290840 a(n) ~ exp(1/2 + n*exp(-1)) * n^n / sqrt(exp(1)-1). - _Vaclav Kotesovec_, Oct 06 2017
%F A290840 a(n) = Sum_{k=0..n} binomial(n,k)*n^(n-k)*k^k. - _Fabian Pereyra_, Jul 16 2024
%F A290840 E.g.f.: 1/((1+LambertW(-x))*(1+LambertW(LambertW(-x)))). - _Fabian Pereyra_, Jul 19 2024
%t A290840 Table[n! * SeriesCoefficient[Exp[n*x]/(1 + LambertW[-x]), {x, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 06 2017 *)
%Y A290840 Main diagonal of A290824.
%Y A290840 Cf. A000312, A207833, A254382.
%K A290840 nonn
%O A290840 0,2
%A A290840 _Ilya Gutkovskiy_, Aug 12 2017