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A308152 G.f.: x * Product_{j>=1, k>=1} ((1 + x^(j*k))/(1 - x^(j*k)))^a(j). 0
1, 2, 8, 32, 138, 612, 2864, 13712, 67416, 337482, 1716208, 8837392, 45997032, 241571408, 1278625480, 6813568656, 36524390042, 196820310100, 1065583770168, 5793299764208, 31615962617272, 173131117881312, 951040865156928, 5239171609158304, 28937688613453048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..25.

FORMULA

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)).

MATHEMATICA

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}]

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]]

CROSSREFS

Cf. A073075, A179467, A308060.

Sequence in context: A150841 A150842 A274483 * A150843 A150844 A141380

Adjacent sequences:  A308149 A308150 A308151 * A308153 A308154 A308155

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 14 2019

STATUS

approved

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Last modified August 2 08:13 EDT 2021. Contains 346422 sequences. (Running on oeis4.)