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Expansion of Product_{k>=1} (1 + 2*k*x^k)/(1 - 2*k*x^k).
3

%I #7 Dec 19 2015 17:05:09

%S 1,4,16,60,192,596,1776,5020,13760,36916,96336,246316,619392,1530548,

%T 3729392,8976364,21337920,50195268,116977232,270114764,618712640,

%U 1406843940,3176387120,7126185948,15894370816,35253947940,77796242768,170868178332,373606888128

%N Expansion of Product_{k>=1} (1 + 2*k*x^k)/(1 - 2*k*x^k).

%H Vaclav Kotesovec, <a href="/A265955/b265955.txt">Table of n, a(n) for n = 0..3280</a>

%F a(n) ~ c * n * 2^n, where c = 2 * Product_{m>=3} (1 + 2/(2^(m-1)/m - 1)) = 193.4198278838721371054040810054045645734538119720773785523616944906739...

%t nmax=40; CoefficientList[Series[Product[(1+2*k*x^k)/(1-2*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A006906, A022629, A032302, A032309, A070933, A265951.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 19 2015