A288098 Convolution inverse of A006171.

1, -1, -2, 0, 0, 4, 1, 3, 0, -5, 0, -7, -6, -4, 7, 0, 6, 9, 11, 10, -2, 13, -13, -10, -17, -20, -25, 0, -11, -11, -2, 11, 41, 27, 41, 17, 58, 12, 27, -21, -2, -36, -67, -52, -59, -95, -75, -20, -89, 35, 0, 62, 41, 142, 97, 172, 63, 154, 148, 85, 110, -36, -17, -156

Offset

0,3

Links

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

Formula

G.f.: Product_{n>=1} E(q^n) where E(q) = Product_{n>=1} (1-q^n).

a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A060640(k)*a(n-k) for n > 0.

G.f.: exp(-Sum_{k>=1} sigma(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Aug 26 2018

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 - x^(i*j)), {i, 1, nmax}, {j, 1, nmax/i}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 28 2018 *)
nmax = 50; CoefficientList[Series[Product[(1 - x^k)^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x]  (* Vaclav Kotesovec, Aug 28 2018 *)
nmax = 50; s = 1 - x; Do[s *= Sum[Binomial[DivisorSigma[0, k], j]*(-1)^j*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]]; , {k, 2, nmax}]; Take[CoefficientList[s, x], nmax] (* Vaclav Kotesovec, Aug 28 2018 *)

Crossrefs

Cf. A006171, A060640, A107742.

Product_{k>=1} (1 - x^k)^sigma_m(k): this sequence (m=0), A288385 (m=1), A288389 (m=2), A288392 (m=3).

Sequence in context: A155039 A238858 A106235 * A118965 A252729 A121552

Adjacent sequences: A288095 A288096 A288097 * A288099 A288100 A288101

Keyword

sign,look

Author

Seiichi Manyama, Jun 05 2017

Status

approved