A320971 - OEIS

%I #21 Sep 08 2022 08:46:23

%S 1,-2,-4,2,10,22,-4,-26,-68,-104,-12,110,378,486,448,-66,-1130,-2242,

%T -3044,-2474,-322,5106,11064,16954,17896,10440,-8032,-40132,-74578,

%U -105754,-108564,-66534,42672,209858,421352,611946,690204,553534,82112,-735082,-1892200

%N Expansion of Product_{k>=1} ((1 - x^k)/(1 + x^k))^(sigma(k)).

%H Seiichi Manyama, <a href="/A320971/b320971.txt">Table of n, a(n) for n = 0..10000</a>

%t With[{nmax=80}, CoefficientList[Series[Product[((1-q^k)/(1+q^k) )^DivisorSigma[1,k], {k, 1, nmax+2}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Oct 29 2018 *)

%o (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-x^k)/(1+x^k))^sigma(k)))

%o (Magma) m:=80; R<q>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(  (&*[((1-q^k)/(1+q^k))^DivisorSigma(1,k): k in [1..(m+2)]]) )); // _G. C. Greubel_, Oct 29 2018

%Y Convolution inverse of A301555.

%Y Product_{k>=1} ((1 - x^k)/(1 + x^k))^(sigma_b(k)): A320908 (b=0), this sequence (b=1), A320972 (b=2).

%Y Cf. A000203, A288385, A288421.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 25 2018