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 A356667 #16 Aug 22 2022 10:06:07
%S A356667 1,1,4,12,72,240,2520,10080,127680,816480,11037600,79833600,
%T A356667 1514177280,12454041600,261655954560,2699348652000,62869385779200,
%U A356667 711374856192000,19407798693803520,243290200817664000,7300765959334848000,102980278869910041600
%N A356667 Expansion of e.g.f. Sum_{k>=0} x^k / (1 - k*x^k/k!).
%F A356667 a(n) = n! * Sum_{d|n} 1/((d-1)!^(n/d-1)) for n > 0.
%F A356667 a(p) = 2 * p! for prime p.
%t A356667 a[n_]:= n! * DivisorSum[n, 1/(# - 1)!^(n/# - 1) &]; a[0] = 1; Array[a, 22, 0] (* _Amiram Eldar_, Aug 22 2022 *)
%o A356667 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^k/k!))))
%o A356667 (PARI) a(n) = if(n==0, 1, n!*sumdiv(n, d, 1/(d-1)!^(n/d-1)));
%Y A356667 Cf. A356632, A356633, A356634.
%Y A356667 Cf. A356668.
%K A356667 nonn
%O A356667 0,3
%A A356667 _Seiichi Manyama_, Aug 22 2022