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 A379993 #14 Feb 05 2025 22:04:21
%S A379993 1,4,28,252,2776,35940,533304,8908228,165247072,3368072196,
%T A379993 74782987240,1796037420804,46379441090448,1281203788073092,
%U A379993 37694510810334616,1176606639075726660,38833052393329645504,1351066066253778043908,49417629820950190273992
%N A379993 Expansion of e.g.f. 1/(1 - x * exp(x))^4.
%F A379993 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+3,3)/(n-k)!.
%F A379993 a(n) == 0 (mod 4) for n>0.
%t A379993 nmax=18;CoefficientList[Series[1/(1 - x * Exp[x])^4,{x,0,nmax}],x]Range[0,nmax]! (* _Stefano Spezia_, Feb 05 2025 *)
%o A379993 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+3, 3)/(n-k)!);
%Y A379993 Cf. A379943, A379994, A379995, A379996.
%Y A379993 Cf. A006153, A377529, A377530.
%K A379993 nonn,easy
%O A379993 0,2
%A A379993 _Seiichi Manyama_, Jan 07 2025