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 A302397 #9 Mar 27 2019 03:51:37
%S A302397 1,-1,0,3,-4,-25,114,287,-4152,1647,192230,-807961,-10164804,
%T A302397 111209111,454840554,-14657978385,21202175504,1988791958879,
%U A302397 -15488971798194,-260886468394153,4872247004699460,23537372210149959,-1365745577227898350,4274609859520565663,364461939727273277016
%N A302397 Expansion of e.g.f. 1/(1 + x*exp(x)).
%H A302397 Seiichi Manyama, <a href="/A302397/b302397.txt">Table of n, a(n) for n = 0..474</a>
%F A302397 E.g.f.: 1/(1 + x*exp(x)).
%F A302397 a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*(n-k)^k/k!.
%F A302397 a(n) = Sum_{k=0..n} (-1)^k*k!*k^(n-k)*binomial(n,k).
%e A302397 1/(1 + x*exp(x)) = 1 - x/1! + 3*x^3/3! - 4*x^4/4! - 25*x^5/5! + 114*x^6/6! + 287*x^7/7! - 4152*x^8/8! + 1647*x^9/9! + ...
%p A302397 a:=series(1/(1+x*exp(x)),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # _Paolo P. Lava_, Mar 26 2019
%t A302397 nmax = 24; CoefficientList[Series[1/(1 + x Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A302397 Join[{1}, Table[n! Sum[(-1)^(n - k) (n - k)^k/k!, {k, 0, n}], {n, 24}]]
%t A302397 Join[{1}, Table[Sum[(-1)^k k! k^(n - k) Binomial[n, k], {k, 0, n}], {n, 24}]]
%Y A302397 Cf. A006153, A009306, A089148.
%K A302397 sign
%O A302397 0,4
%A A302397 _Ilya Gutkovskiy_, Apr 07 2018