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 A356668 #15 Aug 22 2022 10:06:03
%S A356668 1,1,3,7,37,121,1141,5041,60761,378001,5444461,39916801,729041545,
%T A356668 6227020801,130767460825,1321314894901,31388220966961,355687428096001,
%U A356668 9636906872926477,121645100408832001,3649432697160095561,51223991519836175041,1686001091666419279753
%N A356668 Expansion of e.g.f. Sum_{k>=0} x^k / (k! - k*x^k).
%F A356668 Expansion of e.g.f. Sum_{k>=0} x^k / (k! * (1 - k*x^k/k!)).
%F A356668 a(n) = n! * Sum_{d|n} 1/(d * (d-1)!^(n/d)) for n > 0.
%F A356668 a(p) = 1 + p! for prime p.
%t A356668 a[n_]:= n! * DivisorSum[n, 1/(# * (# - 1)!^(n/#)) &]; a[0] = 1; Array[a, 23, 0] (* _Amiram Eldar_, Aug 22 2022 *)
%o A356668 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!-k*x^k))))
%o A356668 (PARI) a(n) = if(n==0, 1, n!*sumdiv(n, d, 1/(d*(d-1)!^(n/d))));
%Y A356668 Cf. A356029, A356328, A356608.
%Y A356668 Cf. A038507, A327578, A356667.
%K A356668 nonn
%O A356668 0,3
%A A356668 _Seiichi Manyama_, Aug 22 2022