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%I #14 Aug 07 2022 12:59:05
%S 1,7,77,1946,84754,6202524,636369348,89979720144,16431405256656,
%T 3796658174518560,1077102230236529760,368915006390671969920,
%U 149873555740938949215360,71297150722148582901815040,39244301012876892023553235200
%N a(n) = n! * Sum_{k=1..n} sigma_k(k)/k.
%F E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - (k*x)^k)/k.
%F a(n) ~ n! * n^(n-1). - _Vaclav Kotesovec_, Aug 07 2022
%t Table[n! * Sum[DivisorSigma[k, k]/k, {k, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 07 2022 *)
%o (PARI) a(n) = n!*sum(k=1, n, sigma(k, k)/k);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k)/(1-x)))
%Y Cf. A023887, A356297, A356436, A356440.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Aug 07 2022
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