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Expansion of Product_{k>=1} ((1 + k*x^k) / (1 - 2*x^k)).
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%I #8 Feb 20 2016 09:06:23

%S 1,3,10,29,77,195,475,1115,2546,5706,12528,27106,57893,122299,255995,

%T 531816,1097377,2252151,4600835,9362334,18990645,38418370,77548880,

%U 156251955,314363615,631703790,1268148900,2543812090,5099469848,10217529291,20464112218

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

%C Convolution of A022629 and A070933.

%H Vaclav Kotesovec, <a href="/A269144/b269144.txt">Table of n, a(n) for n = 0..3290</a>

%F a(n) ~ c * 2^n, where c = Product_{k>=1} (2^k + k)/(2^k - 1) = 19.14883592186082265751161402244824703642181055238186925199088...

%t nmax = 50; CoefficientList[Series[Product[(1+k*x^k)/(1-2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A022629, A070933, A267004, A269153.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 20 2016