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 A338689 #25 Apr 24 2021 09:57:47
%S A338689 1,3,28,223,3126,44660,823544,16514047,387538588,9951176994,
%T A338689 285311670612,8903202187413,302875106592254,11107259264162760,
%U A338689 437894348359764856,18444492187995996159,827240261886336764178,39345059356329821149097
%N A338689 a(n) = Sum_{d|n} (-1)^(d-1) * (n/d)^n * binomial(d+n/d-2, d-1).
%F A338689 G.f.: Sum_{k>=1} (k * x/(1 + (k * x)^k))^k.
%F A338689 If p is prime, a(p) = (-1)^(p-1) + p^p.
%t A338689 a[n_] := DivisorSum[n, (-1)^(# - 1) * (n/#)^n * Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* _Amiram Eldar_, Apr 24 2021 *)
%o A338689 (PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*(n/d)^n*binomial(d+n/d-2, d-1));
%o A338689 (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k*x/(1+(k*x)^k))^k))
%Y A338689 Cf. A217670, A338661, A338684, A338688.
%K A338689 nonn
%O A338689 1,2
%A A338689 _Seiichi Manyama_, Apr 24 2021