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A261582
Expansion of Product_{k>=1} 1/(1 + 3*x^k).
8
1, -3, 6, -21, 69, -201, 591, -1785, 5406, -16194, 48426, -145380, 436641, -1309611, 3927399, -11783280, 35354139, -106059387, 318165729, -954506190, 2863556475, -8590643832, 25771817454, -77315531169, 231946940175, -695840583126, 2087520715788, -6262562872614
OFFSET
0,2
LINKS
FORMULA
a(n) ~ c * (-3)^n, where c = Product_{j>=1} 1/(1-1/(-3)^j) = 1/QPochhammer[-1/3,-1/3] = 0.8212554466473167689981660621182786378...
G.f.: Sum_{i>=0} (-3)^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 13 2018
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[1/(1 + 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[Exp[Sum[(-1)^k*3^k/k*x^k/(1-x^k), {k, 1, nmax}]], {x, 0, nmax}], x]
(O[x]^30 + 4/QPochhammer[-3, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Aug 25 2015
STATUS
approved