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 A003725 M1911 #41 May 17 2025 00:35:10
%S A003725 1,1,-1,-2,9,-4,-95,414,49,-10088,55521,-13870,-2024759,15787188,
%T A003725 -28612415,-616876274,7476967905,-32522642896,-209513308607,
%U A003725 4924388011050,-38993940088199,11731860520780,3807154270837281
%N A003725 E.g.f.: exp( x * exp(-x) ).
%D A003725 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003725 Seiichi Manyama, <a href="/A003725/b003725.txt">Table of n, a(n) for n = 0..557</a>
%H A003725 Bérénice Delcroix-Oger and Clément Dupont, <a href="https://arxiv.org/abs/2505.06094">Lie-operads and operadic modules from poset cohomology</a>, arXiv:2505.06094 [math.CO], 2025. See p. 32, Table 3.
%F A003725 a(n) = Sum_{k=0..n} (-k)^(n-k)*binomial(n, k). - _Vladeta Jovovic_, Mar 15 2003
%F A003725 First column of A215652. - _Peter Bala_, Sep 14 2012
%F A003725 G.f.: Sum_{k>=0} x^k/(1 + k*x)^(k+1). - _Ilya Gutkovskiy_, Jun 25 2018
%t A003725 With[{nn=30},CoefficientList[Series[Exp[x Exp[-x]],{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Oct 20 2011 *)
%o A003725 (PARI) Vec(serlaplace(exp(exp(-x) * x))) \\ _Charles R Greathouse IV_, Sep 26 2017
%Y A003725 Cf. A000248, A069856, A072034. A215652.
%Y A003725 Cf. this sequence (k=1), A292909 (k=2), A292910 (k=3), A292912 (k=4).
%K A003725 sign,easy
%O A003725 0,4
%A A003725 _R. H. Hardin_