A318770 Expansion of Sum_{k>=0} x^(k^2) / Product_{j=1..k} (1 - j*x^j).

1, 1, 1, 1, 2, 2, 4, 4, 8, 9, 17, 19, 38, 42, 80, 97, 174, 208, 389, 460, 826, 1049, 1790, 2248, 3989, 4933, 8451, 11116, 18300, 23742, 40446, 51774, 85774, 115454, 184806, 245967, 406768, 533210, 860295, 1179570, 1850325, 2505585, 4046594, 5407269, 8556317, 11877833, 18327723

Offset: 0

Author

Ilya Gutkovskiy, Sep 03 2018

Keywords

• nonn

Crossrefs

Cf. A193196, A204856, A318771.

Programs

Maple

a:=series(add(x^(k^2)/mul((1-j*x^j),j=1..k),k=0..100),x=0,47): seq(coeff(a,x,n),n=0..46); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 46; CoefficientList[Series[Sum[x^k^2/Product[(1 - j x^j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]