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%I #12 Jan 18 2020 11:51:31
%S 1,-1,0,0,-1,1,-1,0,1,-1,1,0,0,1,0,0,0,1,-1,0,1,-3,2,-1,-3,4,-4,0,3,
%T -5,4,0,-2,4,-1,1,0,3,-2,0,6,-11,9,-1,-13,18,-17,1,13,-23,17,-4,-8,13,
%U -8,7,-6,15,-10,-3,33,-50,42,0,-56,85,-72,6,59,-100,75,-23,-34,53,-44,35
%N Expansion of 1/(1 + x*Product_{k>=1} (1 + x^k)).
%H Seiichi Manyama, <a href="/A318582/b318582.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 1/(1 + x*Sum_{k>=0} A000009(k)*x^k).
%F a(0) = 1; a(n) = -Sum_{k=1..n} A000009(k-1)*a(n-k).
%e G.f. = 1 - x - x^4 + x^5 - x^6 + x^8 - x^9 + x^10 + x^13 + x^17 - x^18 + x^20 - 3*x^21 + ...
%p a:=series(1/(1+x*mul(1+x^k,k=1..100)),x=0,76): seq(coeff(a,x,n),n=0..75); # _Paolo P. Lava_, Apr 02 2019
%t nmax = 75; CoefficientList[Series[1/(1 + x Product[(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = -Sum[PartitionsQ[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]
%Y Cf. similar sequences: A067687, A299105, A299106, A299208, A302017, A318581, A331484.
%Y Cf. A000009, A081362.
%K sign
%O 0,22
%A _Ilya Gutkovskiy_, Aug 29 2018
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