A022664 Expansion of Product_{m>=1} (1 - m*q^m)^4.

1, -4, -2, 16, 9, 4, -90, -56, 12, 60, 700, 232, -51, -1128, -2006, -3648, -2999, 6292, 12004, 19192, 8829, 35024, -43368, -92480, -113859, -227356, -33906, 55072, 569221, 631620, 1193412, 1593152, 1178350, -2589588, -4131366, -6312376, -12864282, -6891608, -10022026, 10270984

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -4, g(n) = n. - Seiichi Manyama, Dec 29 2017

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=4 of A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^4:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 23 2018

Mathematica

With[{nmax=34}, CoefficientList[Series[Product[(1-k*q^k)^4, {k,1,nmax}], {q, 0, nmax}],q]] (* G. C. Greubel, Feb 23 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^4)) \\ G. C. Greubel, Feb 23 2018

Formula

G.f.: exp(-4*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

More terms added by G. C. Greubel, Feb 23 2018