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A022726
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Expansion of 1/Product_{m>=1} (1 - m*q^m)^2.
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3
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1, 2, 7, 18, 49, 114, 282, 624, 1422, 3058, 6597, 13700, 28564, 57698, 116479, 230398, 453698, 879080, 1696732, 3230578, 6124326, 11486884, 21439480, 39659598, 73036175, 133445640, 242756058, 438680734, 789328034, 1411926186, 2515574329, 4458203590, 7871211452, 13831782146
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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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a(n) ~ c * n * 3^(n/3), where
c = 9588921272.54120308291761424720457... = (c0^2 + 2*c1*c2)/3 if mod(n,3)=0
c = 9588921272.50566179874517327053929... = (c2^2 + 2*c0*c1)/3 if mod(n,3)=1
c = 9588921272.49785814355801212400055... = (c1^2 + 2*c0*c2)/3 if mod(n,3)=2
For the constants c0, c1, c2 see A006906.
(End)
G.f.: exp(2*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[1/(1-k*x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 06 2016 *)
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PROG
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(PARI)
N=66; q='q+O('q^N);
gf= 1/prod(n=1, N, (1-n*q^n)^2 );
Vec(gf)
(Magma) n:=40; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^2:m in [1..n]])); // G. C. Greubel, Jul 25 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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