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%I #22 Aug 11 2018 21:57:00
%S 1,-2,-2,2,3,6,-1,-2,-10,-14,-7,-2,11,26,43,30,28,-6,-40,-92,-128,
%T -132,-115,-48,54,200,339,484,499,476,274,-32,-501,-998,-1539,-1924,
%U -2042,-1838,-1139,12,1664,3540,5588,7258,8392,8230,6812,3480,-1472,-8150,-15737,-23670,-30478
%N Expansion of Product_{k>=1} (1 - x^k)^(k+1).
%C Convolution of A010815 and A073592.
%C Convolution inverse of A005380.
%F G.f.: exp(-Sum_{k>=1} (sigma_1(k) + sigma_2(k))*x^k/k).
%t nmax = 52; CoefficientList[Series[Product[(1 - x^k)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 52; CoefficientList[Series[Exp[-Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[d (d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 52}]
%Y Cf. A005380, A010815, A073592, A092346.
%K sign
%O 0,2
%A _Ilya Gutkovskiy_, Aug 11 2018
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