OFFSET
0,2
COMMENTS
Convolution inverse of A305050.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=1} ((1 - x^k)/(1 + x^k))^A007425(k).
G.f.: Product_{k>=1} theta_4(x^k)^tau(k), where theta_4() is the Jacobi theta function and tau() is the number of divisors. - Ilya Gutkovskiy, May 18 2019
MATHEMATICA
With[{nmax=50}, CoefficientList[Series[Product[(1 - x^(i*j*k))/(1 + x^(i*j*k)), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}], {x, 0, nmax}], x]] (* G. C. Greubel, Nov 01 2018 *)
PROG
(PARI) m=50; x='x+O('x^m); Vec(prod(k=1, m, ((1-x^k)/(1+x^k))^sumdiv(k, x, sumdiv(x, y, 1 )))) \\ G. C. Greubel, Nov 01 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(&*[(&*[(1 - x^(i*j*k))/(1 + x^(i*j*k)): i in [1..m]]): j in [1..m]]): k in [1..m]]))); // G. C. Greubel, Nov 01 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Nov 01 2018
STATUS
approved