A320971 Expansion of Product_{k>=1} ((1 - x^k)/(1 + x^k))^(sigma(k)).

1, -2, -4, 2, 10, 22, -4, -26, -68, -104, -12, 110, 378, 486, 448, -66, -1130, -2242, -3044, -2474, -322, 5106, 11064, 16954, 17896, 10440, -8032, -40132, -74578, -105754, -108564, -66534, 42672, 209858, 421352, 611946, 690204, 553534, 82112, -735082, -1892200

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Mathematica

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 *)

Prog

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

Crossrefs

Convolution inverse of A301555.

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

Cf. A000203, A288385, A288421.

Sequence in context: A259707 A335866 A247085 * A360667 A342828 A286958

Adjacent sequences: A320968 A320969 A320970 * A320972 A320973 A320974

Keyword

sign

Author

Seiichi Manyama, Oct 25 2018

Status

approved