|
%I #16 Sep 08 2022 08:46:23
%S 1,-1,-1,0,1,0,0,0,1,0,-1,-1,1,1,-1,-2,2,2,-1,-2,0,1,-1,0,1,2,0,-2,-2,
%T 2,-1,0,1,2,-1,-1,0,2,-3,-2,1,3,-1,0,1,3,-3,-4,0,4,1,-3,1,2,-1,-4,-1,
%U 5,2,-4,0,3,1,-3,-1,0,1,-3,1,3,3,-2,-2,-2,1,-1,1,1,3,-3
%N Expansion of Product_{k>0} (1-x^p(k)), where p(k) is the number of partitions of k (A000041).
%H Seiichi Manyama, <a href="/A320844/b320844.txt">Table of n, a(n) for n = 0..10000</a>
%t CoefficientList[Series[Product[1 - x^PartitionsP[k], {k, 1, 120}], {x, 0, 100}], x] (* _G. C. Greubel_, Oct 27 2018 *)
%o (PARI) x='x+O('x^50); Vec(prod(k=1,50, 1-x^numbpart(k))) \\ _G. C. Greubel_, Oct 27 2018
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[1-x^NumberOfPartitions(k): k in [1..100]]))); // _G. C. Greubel_, Oct 27 2018
%Y Convolution inverse of A007279.
%Y Cf. A000041, A280253.
%K sign,look
%O 0,16
%A _Seiichi Manyama_, Oct 22 2018
|
