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A308152 G.f.: x * Product_{j>=1, k>=1} ((1 + x^(j*k))/(1 - x^(j*k)))^a(j). 0

%I

%S 1,2,8,32,138,612,2864,13712,67416,337482,1716208,8837392,45997032,

%T 241571408,1278625480,6813568656,36524390042,196820310100,

%U 1065583770168,5793299764208,31615962617272,173131117881312,951040865156928,5239171609158304,28937688613453048

%N G.f.: x * Product_{j>=1, k>=1} ((1 + x^(j*k))/(1 - x^(j*k)))^a(j).

%F G.f. A(x) satisfies: A(x) = x * exp(2 * Sum_{i>=1} Sum_{j>=1} A(x^(i*(2*j-1)))/(2*j - 1)).

%t a[n_] := a[n] = SeriesCoefficient[x Product[Product[((1 + x^(j k))/(1 - x^(j k)))^a[j], {k, 1, n - 1}], {j, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 25}]

%t terms = 25; A[_] = 0; Do[A[x_] = x Exp[2 Sum[Sum[A[x^(i (2 j - 1))]/(2 j - 1), {j, 1, terms}], {i, 1,terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]

%Y Cf. A073075, A179467, A308060.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, May 14 2019

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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)