A022662 Expansion of Product_{m>=1} (1 - m*q^m)^2.

1, -2, -3, 2, 4, 16, -3, 6, -31, -72, -15, -44, 9, 154, 521, 48, 426, 66, 2, -1618, -3782, -210, -3882, -1282, 1119, 3940, 10867, 37208, 11647, 20574, 6256, 534, -1915, -120006, -161755, -312622, -93923, -271850, -25782, -197026, 1112303, 574604, 209604, 3038822, 4187500, 1398330

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A022662, A022726.

Column k=2 of A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^2:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 18 2018

Mathematica

nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = -2; poly[[3]] = 1; Do[Do[Do[poly[[j+1]] -= k*poly[[j-k+1]], {j, nmax, k, -1}];, {p, 1, 2}], {k, 2, nmax}]; poly  (* Vaclav Kotesovec, Jan 07 2016 *)
With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^2, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 18 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^2)) \\ G. C. Greubel, Feb 18 2018

Formula

G.f.: exp(-2*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018