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%I #11 Aug 23 2019 20:48:30
%S 1,2,8,22,68,170,484,1166,3048,7274,18000,41806,100684,229258,535692,
%T 1206230,2758944,6123650,13798088,30284894,67272756,146426002,
%U 321513284,693944814,1510245960,3236648578,6985572672,14885926182,31904642348,67618415690
%N Expansion of Product_{k>=1} 1/(1 - 2*k*x^k).
%H Vaclav Kotesovec, <a href="/A265951/b265951.txt">Table of n, a(n) for n = 0..3280</a>
%F a(n) ~ c * n * 2^n, where c = 1/2 * Product_{m>=3} 1/(1 - m/2^(m-1)) = 9.281573281805057363737677116134642024212942973614535341005126953773818...
%p b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p 2^n, b(n, i-1) +i*2*b(n-i, min(n-i, i)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..32); # _Alois P. Heinz_, Aug 23 2019
%t nmax=40; CoefficientList[Series[Product[1/(1-2*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A006906, A265974, A265975, A265976.
%Y Cf. A032309, A070933, A265955.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 19 2015
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