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 A319218 #8 Jan 09 2019 09:19:18
%S A319218 1,-1,-2,3,8,75,-216,-175,-3816,-36225,189800,325149,2375460,25547951,
%T A319218 386162126,-3290670825,-6316583056,-59290501809,-310987223208,
%U A319218 -4836373835707,-86500419684420,1119358992256239,3043733432729198,26408738842522959,169835931388147464
%N A319218 Expansion of e.g.f. Product_{k>=1} (1 - x^k/(k - 1)!).
%F A319218 E.g.f.: exp(-Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*((j - 1)!)^k)).
%p A319218 seq(n!*coeff(series(mul((1 - x^k/(k - 1)!),k=1..100),x=0,25),x,n),n=0..24); # _Paolo P. Lava_, Jan 09 2019
%t A319218 nmax = 24; CoefficientList[Series[Product[(1 - x^k/(k - 1)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A319218 nmax = 24; CoefficientList[Series[Exp[-Sum[Sum[x^(j k)/(k (j - 1)!^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A319218 a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[-d (d - 1)!^(-k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 24}]
%Y A319218 Cf. A032299, A076900, A185895, A319219.
%K A319218 sign
%O A319218 0,3
%A A319218 _Ilya Gutkovskiy_, Sep 13 2018