A374076 - OEIS

%I #6 Jun 28 2024 14:01:21

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

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

%U 11,-6,-3,10,-14,12,-5,-6,15,-17,14,-4,-10,19,-21,15,-1,-15,25,-25

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

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

%t a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 4 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]

%Y Cf. A081360, A081362, A109700, A281243, A284317, A374064, A374065, A374077, A374078, A374079.

%K sign

%O 0,19

%A _Ilya Gutkovskiy_, Jun 27 2024