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A261582 Expansion of Product_{k>=1} 1/(1 + 3*x^k). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2094

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

Cf. A032308, A242587, A246935, A261565, A261567.

Sequence in context: A054878 A084567 A294527 * A135686 A218244 A151961

Adjacent sequences:  A261579 A261580 A261581 * A261583 A261584 A261585

KEYWORD

sign

AUTHOR

Vaclav Kotesovec, Aug 25 2015

STATUS

approved

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Last modified January 23 13:38 EST 2020. Contains 331171 sequences. (Running on oeis4.)