A320971 -id:A320971 - cp's OEIS frontend

A320972 Expansion of Product_{k>=1} ((1 - x^k)/(1 + x^k))^(sigma_2(k)).

1, -2, -8, -2, 30, 110, 92, -182, -976, -2064, -1488, 3714, 17618, 35814, 37680, -25278, -216910, -541538, -819268, -480334, 1441634, 5924858, 12518720, 16883366, 7972200, -32275008, -120780700, -250726492, -349220282, -229745138, 424373412, 1958370998, 4418456156

Offset: 0

Seiichi Manyama, Oct 25 2018

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

Convolution inverse of A301556.
Product_{k>=1} ((1 - x^k)/(1 + x^k))^(sigma_b(k)): A320908 (b=0), A320971 (b=1), this sequence (b=2).
Cf. A001157, A288389, A288422.

N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-x^k)/(1+x^k))^sigma(k, 2)))

A321068 a(n) = [x^n] Product_{k>=1} ((1 - x^k)/(1 + x^k))^sigma_n(k).

Original entry on oeis.org

1, -2, -8, -22, 294, 24982, 1372372, 10145326, -38651841784, -21995644478504, -5088041946350856, 29713279339187796814, 155715351422115081062330, 370606511915720675179342334, -12360092915168107023209454901320

Offset: 0

Seiichi Manyama, Oct 26 2018

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Seiichi Manyama, Table of n, a(n) for n = 0..80

Cf. A320908, A320971, A320972, A321042, A321057.

Table[SeriesCoefficient[Product[((1 - x^k)/(1 + x^k))^DivisorSigma[n, k], {k, 1, n}], {x, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Oct 27 2018 *)

{a(n) = polcoeff(prod(k=1, n, ((1-x^k+x*O(x^n))/(1+x^k+x*O(x^n)))^sigma(k, n)), n)}

cp's OEIS Frontend

A320972 Expansion of Product_{k>=1} ((1 - x^k)/(1 + x^k))^(sigma_2(k)).

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