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%I #9 Apr 02 2019 05:54:10
%S 1,-1,-3,0,0,9,5,4,-1,-27,-2,-33,-17,8,43,92,36,100,-8,-11,-136,-120,
%T -296,-363,-13,-203,286,306,1010,667,724,790,151,-258,-1207,-964,
%U -3325,-2059,-2924,-1992,-2116,1277,3625,4437,7724,7734,11524,5801,9685,-855,-2799,-13409,-16423
%N Expansion of Product_{i>=1, j>=1, k>=1} (1 - x^(i*j*k)).
%H Seiichi Manyama, <a href="/A319359/b319359.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Product_{k>=1} (1 - x^k)^A007425(k).
%F G.f.: exp(-Sum_{k>=1} A174466(k)*x^k/k).
%p a:=series(mul(mul(mul(1-x^(i*j*k),k=1..55),j=1..55),i=1..55),x=0,53): seq(coeff(a,x,n),n=0..52); # _Paolo P. Lava_, Apr 02 2019
%t nmax = 52; CoefficientList[Series[Product[(1 - x^(i j k)), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}], {x, 0, nmax}], x]
%t nmax = 52; CoefficientList[Series[Product[(1 - x^k)^Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, nmax}], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[d DivisorSigma[1, k/d] DivisorSigma[0, d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 52}]
%Y Cf. A000005, A000203, A007425, A174465, A174466, A280473, A288098.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Sep 17 2018
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