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 A163191 #7 Aug 15 2023 02:08:54
%S A163191 1,0,1,8,82,1024,15690,279936,5771363,134218240,3487832978,
%T A163191 100000000000,3138673052884,106993205379072,3937454749863386,
%U A163191 155568096631586816,6568441588686506948,295147905179352825856,14063102470280932000763,708235345355337676357632
%N A163191 a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n,k)*sigma(n,k) for n>0 with a(0)=1.
%C A163191 Definition: sigma(n,k)= sigma_k(n) = Sum_{d|n} d^k.
%F A163191 a(n) = Sum_{d|n} (d-1)^n for n>0 with a(0)=1.
%t A163191 a[0] = 1; a[n_] := DivisorSum[n, (#-1)^n &]; Array[a, 20, 0] (* _Amiram Eldar_, Aug 15 2023 *)
%o A163191 (PARI) {a(n)=if(n==0,1,sumdiv(n,d,(d-1)^n))}
%o A163191 (PARI) {a(n)=if(n==0,1,sum(k=0,n,(-1)^(n-k)*binomial(n,k)*sigma(n,k)))}
%Y A163191 Cf. A163190 (variant), A000203 (sigma).
%K A163191 nonn
%O A163191 0,4
%A A163191 _Paul D. Hanna_, Jul 22 2009