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%I #6 Jun 28 2024 14:00:57
%S 1,0,0,-1,0,0,1,0,-1,-1,0,1,1,-1,-1,-1,2,1,0,-2,-1,1,2,0,-2,-2,2,2,1,
%T -3,-2,1,4,1,-3,-4,2,4,3,-5,-5,0,7,4,-4,-8,0,7,8,-5,-9,-4,10,9,-3,-13,
%U -5,9,14,-3,-14,-10,12,16,1,-19,-12,10,23,1,-20,-20,13,26,8,-26
%N Expansion of Product_{k>=1} 1 / (1 + x^(5*k-2)).
%t nmax = 75; CoefficientList[Series[Product[1/(1 + x^(5 k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 3 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]
%Y Cf. A081360, A081362, A109699, A281271, A284320, A374064, A374065, A374076, A374078, A374079.
%K sign
%O 0,17
%A _Ilya Gutkovskiy_, Jun 27 2024