|
%I #17 Apr 13 2018 21:52:37
%S 1,-3,6,-21,69,-201,591,-1785,5406,-16194,48426,-145380,436641,
%T -1309611,3927399,-11783280,35354139,-106059387,318165729,-954506190,
%U 2863556475,-8590643832,25771817454,-77315531169,231946940175,-695840583126,2087520715788,-6262562872614
%N Expansion of Product_{k>=1} 1/(1 + 3*x^k).
%H Seiichi Manyama, <a href="/A261582/b261582.txt">Table of n, a(n) for n = 0..2094</a>
%F a(n) ~ c * (-3)^n, where c = Product_{j>=1} 1/(1-1/(-3)^j) = 1/QPochhammer[-1/3,-1/3] = 0.8212554466473167689981660621182786378...
%F G.f.: Sum_{i>=0} (-3)^i*x^i/Product_{j=1..i} (1 - x^j). - _Ilya Gutkovskiy_, Apr 13 2018
%t nmax = 40; CoefficientList[Series[Product[1/(1 + 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 40; CoefficientList[Series[Exp[Sum[(-1)^k*3^k/k*x^k/(1-x^k), {k, 1, nmax}]], {x, 0, nmax}], x]
%t (O[x]^30 + 4/QPochhammer[-3, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y Cf. A032308, A242587, A246935, A261565, A261567.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Aug 25 2015
|
