A022663 Expansion of Product_{m>=1} (1 - m*q^m)^3.

1, -3, -3, 8, 9, 18, -35, -33, -66, -91, 216, 189, 386, 315, 333, -1483, -2268, -2214, -1883, -456, -801, 23032, 12186, 22665, 18622, -20328, -39549, -78834, -146838, -249342, -146662, 15678, 564771, 238159, 1274913, 1398063, 1572593, 1423266, -833778, -3484732, -5261736, -9671502

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) = -3, g(n) = n. - Seiichi Manyama, Dec 29 2017

Links

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

Crossrefs

Column k=3 of A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^3: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)^3, {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)^3)) \\ G. C. Greubel, Feb 23 2018

Formula

G.f.: exp(-3*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