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A091360
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Partial sums of A000219.
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15
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1, 2, 5, 11, 24, 48, 96, 182, 342, 624, 1124, 1983, 3462, 5947, 10114, 16993, 28290, 46624, 76225, 123555, 198833, 317627, 504102, 794885, 1246079, 1942112, 3010857, 4643515, 7126749, 10886361, 16555324, 25067633, 37801062, 56776035, 84951990, 126643036, 188127997, 278507781, 410949776, 604437277, 886284200, 1295668181
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Euler transform of 2, 2, 3, 4, 5, 6, 7, 8, 9, ...
G.f.: 1/( (1-x) * prod(n>=1, (1-x^n)^n ) ). [Joerg Arndt, Mar 15 2014]
a(n) ~ (n/(2*Zeta(3)))^(1/3) * A000219(n).
a(n) ~ exp(1/12 + 3 * Zeta(3)^(1/3) * n^(2/3) / 2^(2/3)) / (A * 2^(23/36) * sqrt(3*Pi) * Zeta(3)^(5/36) * n^(13/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
(End)
G.f.: exp(Sum_{k>=1} (sigma_2(k) + 1)*x^k/k). - Ilya Gutkovskiy, Aug 21 2018
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MATHEMATICA
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CoefficientList[Series[1/(1-x)*Product[1/(1-x^k)^k, {k, 1, 50}], {x, 0, 50}], x] (* Vaclav Kotesovec, Aug 16 2015 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec( 1/((1-x)*prod(n=1, N, (1-x^n)^n )) ) \\ Joerg Arndt, Mar 15 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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