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 A354509 #15 Aug 16 2022 10:21:13
%S A354509 1,2,6,5,5,-8,560,-5997,-14765,176826,5206410,-42491623,-427057527,
%T A354509 -412183484,147180377804,-569782989113,-8367671807033,
%U A354509 -119681999820906,4440973420854454,-121033449284728099,49772248126885197,36615485147317407728,1696495197400394891912
%N A354509 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(d+1)/(d * (k/d)!) )/(n-k)!.
%F A354509 a(n) = Sum_{k=1..n} A352013(k) * binomial(n,k).
%F A354509 E.g.f.: -exp(x) * Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k.
%F A354509 E.g.f.: exp(x) * Sum_{k>0} log(1+x^k)/k!.
%o A354509 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!))/(n-k)!);
%o A354509 (PARI) a352013(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
%o A354509 a(n) = sum(k=1, n, a352013(k)*binomial(n, k));
%o A354509 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, (-1)^k*(exp(x^k)-1)/k)))
%o A354509 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, log(1+x^k)/k!)))
%Y A354509 Cf. A352013, A354505, A356401.
%K A354509 sign
%O A354509 1,2
%A A354509 _Seiichi Manyama_, Aug 15 2022