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%I #28 Jul 03 2021 07:17:52
%S 1,-1,-1,2,0,29,-135,727,-1967,-6074,94510,1548051,-41361089,
%T 408842095,213929807,-41951737904,130060640466,10569226878107,
%U -229371598130229,3327344803563111,-31418096993670379,-383829978086171112,17799865170898698140,220582224147105677385
%N E.g.f.: Product_{k>=1} (1 - x^k)^(1/k!).
%H Seiichi Manyama, <a href="/A345762/b345762.txt">Table of n, a(n) for n = 0..451</a>
%F E.g.f.: exp( -Sum_{k>=1} (exp(x^k) - 1)/k ).
%F E.g.f.: exp( -Sum_{k>=1} A087906(k)*x^k/k! ).
%F a(n) = -(n-1)! * Sum_{k=1..n} (Sum_{d|k} 1/(d-1)!) * a(n-k)/(n-k)! for n > 0.
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1-x^k)^(1/k!))))
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, (exp(x^k)-1)/k))))
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, 1/(d-1)!)*x^k/k))))
%o (PARI) a(n) = if(n==0, 1, -(n-1)!*sum(k=1, n, sumdiv(k, d, 1/(d-1)!)*a(n-k)/(n-k)!));
%Y Cf. A028343, A087906, A185895, A209902, A330199, A345758, A346039, A346057.
%K sign
%O 0,4
%A _Seiichi Manyama_, Jun 26 2021
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