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A320590 Expansion of Product_{k>=1} 1/(1 - x^k/(1 + x)^k). 3
1, 1, 1, 0, 1, -2, 5, -12, 28, -63, 137, -290, 604, -1253, 2617, -5537, 11870, -25666, 55617, -120103, 257582, -548119, 1158437, -2437114, 5117165, -10748530, 22621055, -47728657, 100932549, -213750621, 452855190, -958925784, 2028187595, -4283531490, 9033779224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: exp(Sum_{k>=1} x^k/(k*((1 + x)^k - x^k))).

G.f.: exp(Sum_{k>=1} sigma(k)*x^k/(k*(1 + x)^k)).

MAPLE

seq(coeff(series(mul(1/(1-x^k/(1+x)^k), k=1..n), x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 16 2018

MATHEMATICA

nmax = 34; CoefficientList[Series[Product[1/(1 - x^k/(1 + x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 34; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] x^k/(k (1 + x)^k), {k, 1, nmax}]], {x, 0, nmax}], x]

PROG

(PARI) m=50; x='x+O('x^m); Vec(prod(k=1, m+2, 1/(1 - x^k/(1 + x)^k))) \\ G. C. Greubel, Oct 29 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1 - x^k/(1 + x)^k): k in [1..(m+2)]]) )); // G. C. Greubel, Oct 29 2018

CROSSREFS

Cf. A000203, A103446, A218482, A320568, A320591.

Sequence in context: A118898 A111586 A192657 * A006979 A019301 A006980

Adjacent sequences:  A320587 A320588 A320589 * A320591 A320592 A320593

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Oct 16 2018

STATUS

approved

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Last modified October 20 05:49 EDT 2019. Contains 328247 sequences. (Running on oeis4.)