A022640 Expansion of Product_{m>=1} (1 + m*q^m)^12.

1, 12, 90, 544, 2823, 13116, 55982, 222936, 838011, 2998896, 10282986, 33959016, 108458924, 336141084, 1013801700, 2982628712, 8577246237, 24152726184, 66699488360, 180885417408, 482312100000, 1265779076680, 3272696917782, 8343402502128, 20989675199987, 52143220175940

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=12 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^12:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 17 2018

Maple

[seq(coeff(series(mul((1+m*q^m)^(12), m=1..100),q,101),q,j),j=0..25)]; # Muniru A Asiru, Feb 18 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^12, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 17 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^12)) \\ G. C. Greubel, Feb 17 2018