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%I #4 May 18 2018 19:48:38
%S 1,-1,-1,-1,0,1,-1,4,2,3,1,8,-8,10,-8,-9,-15,-6,-46,-14,-65,-28,14,
%T -29,-43,-37,298,59,234,165,738,354,1083,703,1944,-2024,1917,-1085,
%U 3658,-2385,-6421,-7220,118,-15569,-11604,-19162,-9448,-36140,-24561,-50505,-24807,47645
%N Expansion of Product_{k>=1} (1 - q(k)*x^k), where q(k) = number of partitions of k into distinct parts (A000009).
%C Convolution inverse of A270995.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionQ.html">Partition Function Q</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} (1 - A000009(k)*x^k).
%t nmax = 51; CoefficientList[Series[Product[(1 - PartitionsQ[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, Sum[-Sum[d PartitionsQ[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 51}]
%Y Cf. A000009, A270995, A271619, A304783, A304785.
%K sign
%O 0,8
%A _Ilya Gutkovskiy_, May 18 2018
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