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%I #16 May 27 2018 19:46:15
%S 1,-1,-1,1,2,26,-6,414,-624,-288,-20880,164880,-9756000,43529760,
%T -324404640,-4052492640,-48521410560,1168445053440,-26858914467840,
%U 341240066334720,-5752671815116800,49267037136844800,-769468911734476800,39863275492626432000
%N E.g.f.: Product_{k>=1} (1 - x^k/k).
%H Seiichi Manyama, <a href="/A292359/b292359.txt">Table of n, a(n) for n = 0..451</a>
%F Conjecture: a(n) ~ -(-1)^n * n! / n^2. - _Vaclav Kotesovec_, Sep 15 2017
%F E.g.f.: exp(-Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*j^k)). - _Ilya Gutkovskiy_, May 27 2018
%t nmax = 20; CoefficientList[Series[Product[(1 - x^k/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 15 2017 *)
%o (PARI) {a(n) = n!*polcoeff(prod(k=1, n, 1-x^k/k+x*O(x^n)), n)}
%Y Cf. A007838, A007841.
%K sign
%O 0,5
%A _Seiichi Manyama_, Sep 14 2017