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%I #9 Aug 08 2022 09:39:53
%S 1,7,40,281,2006,17677,159020,1678721,18555850,230978981,2979853592,
%T 43323807265,644160764846,10543905398405,178896116995276,
%U 3284281839169217,61879477543508690,1264313089711322821,26333205612282941600,588074615109602665601
%N a(n) = n! * Sum_{k=1..n} Sum_{d|k} d/(k/d)!.
%F a(n) = n! * Sum_{k=1..n} A354863(k)/k!.
%F E.g.f.: (1/(1-x)) * Sum_{k>0} k * (exp(x^k) - 1).
%o (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, d/(k/d)!));
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k*(exp(x^k)-1))/(1-x)))
%Y Cf. A354863, A355886, A356009.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Aug 08 2022
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