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 A338688 #24 Apr 24 2021 09:57:37
%S A338688 1,1,4,-5,6,2,8,-121,172,44,12,-759,14,566,5536,-7665,18,-6877,20,
%T A338688 2744,70862,21218,24,-570573,218776,104324,918568,942479,30,-3693495,
%U A338688 32,-9408481,11779582,2223344,19935756,-15628120,38,9954650,145283360,-371959011,42,-382916059
%N A338688 a(n) = - Sum_{d|n} (-n/d)^d * binomial(d+n/d-2, d-1).
%F A338688 G.f.: Sum_{k>=1} k * (x/(1 + k * x^k))^k.
%F A338688 If p is prime, a(p) = (-1)^(p-1) + p.
%t A338688 a[n_] := -DivisorSum[n, (-n/#)^# * Binomial[# + n/# - 2, # - 1] &]; Array[a, 40] (* _Amiram Eldar_, Apr 24 2021 *)
%o A338688 (PARI) a(n) = -sumdiv(n, d, (-n/d)^d*binomial(d+n/d-2, d-1));
%o A338688 (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k*(x/(1+k*x^k))^k))
%Y A338688 Cf. A217670, A324159, A338683, A338689.
%K A338688 sign
%O A338688 1,3
%A A338688 _Seiichi Manyama_, Apr 24 2021