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 A354890 #17 Jun 11 2022 07:52:03
%S A354890 1,6,33,472,3245,157896,828583,132078976,1578211209,307174074400,
%T A354890 285351587411,1835340563252736,302881333613053,11743240652094910336,
%U A354890 336123967242674523375,149825956013958069846016,827240617573764860177,3551697093896307129060647424
%N A354890 a(n) = n! * Sum_{d|n} d^n / d!.
%H A354890 Seiichi Manyama, <a href="/A354890/b354890.txt">Table of n, a(n) for n = 1..284</a>
%F A354890 E.g.f.: Sum_{k>0} (k * x)^k/(k! * (1 - (k * x)^k)).
%F A354890 If p is prime, a(p) = p^p + p! = A053042(p).
%t A354890 a[n_] := n! * DivisorSum[n, #^n/#! &]; Array[a, 18] (* _Amiram Eldar_, Jun 10 2022 *)
%o A354890 (PARI) a(n) = n!*sumdiv(n, d, d^n/d!);
%o A354890 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!*(1-(k*x)^k)))))
%Y A354890 Cf. A053042, A354888, A354891, A354892.
%K A354890 nonn
%O A354890 1,2
%A A354890 _Seiichi Manyama_, Jun 10 2022