A022630 Expansion of Product_{m>=1} (1 + m*q^m)^2.

1, 2, 5, 14, 28, 64, 133, 266, 513, 1000, 1873, 3420, 6257, 11078, 19585, 34192, 58714, 99870, 168858, 281666, 467082, 768994, 1253038, 2030658, 3269551, 5227868, 8304467, 13133256, 20630535, 32250274, 50181624, 77653530, 119634925, 183532470, 280245365

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=2 of A297321.

Cf. A022629, A022694.

Programs

Magma

Coefficients(&*[(1+m*x^m)^2:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 16 2018

Mathematica

nn=34; CoefficientList [Series[ Product[(1 + m*q^m)^2, {m, nn}], {q, 0, nn}],q] (* Robert G. Wilson v, Feb 08 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^2)) \\ G. C. Greubel, Feb 16 2018

Formula

Self-convolution of A022629. - Alois P. Heinz, Dec 28 2017

G.f.: exp(2*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018