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Expansion of Product_{k>=1} 1 / (1 + x^(5*k-4)).
3

%I #6 Jun 28 2024 14:01:05

%S 1,-1,1,-1,1,-1,0,0,0,0,0,-1,2,-2,2,-2,1,0,-1,1,-1,0,2,-3,4,-4,3,-1,

%T -1,2,-3,2,1,-4,6,-7,7,-4,0,3,-5,5,-2,-3,8,-11,12,-9,3,3,-8,10,-7,0,8,

%U -15,19,-17,9,1,-10,16,-15,6,7,-19,28,-29,20,-5,-11,23,-26,17,1,-21

%N Expansion of Product_{k>=1} 1 / (1 + x^(5*k-4)).

%t nmax = 75; CoefficientList[Series[Product[1/(1 + x^(5 k - 4)), {k, 1, nmax}], {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 1 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]

%Y Cf. A081360, A081362, A109697, A280454, A284314, A374064, A374065, A374076, A374077, A374078.

%K sign

%O 0,13

%A _Ilya Gutkovskiy_, Jun 27 2024