A301556 -id:A301556 - 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

sign

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)))

A321057 a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 - x^k))^sigma_n(k).

Original entry on oeis.org

1, 2, 12, 94, 1522, 48154, 3087600, 377880794, 93356591804, 46415548879976, 44773963087975388, 86770399797767582434, 340765670578000502365102, 2625605734866823121935402410, 40755373130582885082115865730892, 1290109927277547765958474680645604818

Offset: 0

Seiichi Manyama, Oct 26 2018

nonn

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

Cf. A301554, A301555, A301556, A319647, A321042, A321068.

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)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI