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 A356459 #13 Aug 12 2025 06:40:18
%S A356459 1,7,40,281,2006,17677,159020,1678721,18555850,230978981,2979853592,
%T A356459 43323807265,644160764846,10543905398405,178896116995276,
%U A356459 3284281839169217,61879477543508690,1264313089711322821,26333205612282941600,588074615109602665601
%N A356459 a(n) = n! * Sum_{k=1..n} Sum_{d|k} d/(k/d)!.
%F A356459 a(n) = n! * Sum_{k=1..n} A354863(k)/k!.
%F A356459 E.g.f.: (1/(1-x)) * Sum_{k>0} k * (exp(x^k) - 1).
%F A356459 Conjecture: a(n) ~ c * n! * n^2, where c = 0.5732... - _Vaclav Kotesovec_, Aug 12 2025
%t A356459 Table[n! * Sum[Sum[d/(k/d)!, {d,Divisors[k]}], {k,1,n}], {n,1,20}] (* _Vaclav Kotesovec_, Aug 11 2025 *)
%o A356459 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, d/(k/d)!));
%o A356459 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k*(exp(x^k)-1))/(1-x)))
%Y A356459 Cf. A354863, A355886, A356009.
%K A356459 nonn
%O A356459 1,2
%A A356459 _Seiichi Manyama_, Aug 08 2022