|
%I #8 Nov 21 2015 00:45:07
%S 1,4,12,36,92,228,540,1236,2748,6004,12876,27252,57036,118308,243564,
%T 498564,1015484,2060484,4167804,8409588,16934748,34049940,68378220,
%U 137185428,275026476,551052676,1103618508,2209525092,4422484764,8850120420,17707920924
%N Expansion of Product_{k>=1} (1 + 2*x^k)/(1 - 2*x^k).
%F a(n) = c * 2^n, where c = 1/(A048651 * A083864) = 2*Product_{j>=1} (2^j+1)/(2^j-1) = 16.5119758715565001310882816988645462530540032335764606912075051272567456...
%t nmax = 40; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 40; CoefficientList[Series[Exp[Sum[2^(2*k)/(2*k-1)*x^(2*k-1)/(1 - x^(2*k-1)), {k, 1, nmax}]], {x, 0, nmax}], x]
%t (O[x]^30 - QPochhammer[-2, x]/(3 QPochhammer[2, x]))[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y Cf. A032302, A070933, A261563.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 25 2015
|
