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%I #6 Jun 28 2024 14:01:01
%S 1,0,-1,0,1,0,-1,-1,1,1,-1,-1,0,1,1,-1,-1,0,1,1,-1,-2,0,2,2,-2,-3,1,4,
%T 1,-4,-3,3,4,0,-5,-3,4,5,-1,-6,-3,6,6,-2,-8,-3,8,8,-5,-11,-2,12,8,-8,
%U -13,1,15,8,-12,-15,3,19,7,-16,-17,6,23,8,-22,-20,11,30,5,-30,-22
%N Expansion of Product_{k>=1} 1 / (1 + x^(5*k-3)).
%t nmax = 75; CoefficientList[Series[Product[1/(1 + x^(5 k - 3)), {k, 1, nmax}], {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 2 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]
%Y Cf. A081360, A081362, A109698, A281272, A284319, A374064, A374065, A374076, A374077, A374079.
%K sign
%O 0,22
%A _Ilya Gutkovskiy_, Jun 27 2024
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