A318771 Expansion of Sum_{k>=0} x^(k^2) / Product_{j=1..k} (1 - x^j)^j.

1, 1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 22, 25, 37, 47, 64, 81, 113, 140, 191, 243, 319, 408, 540, 677, 889, 1132, 1462, 1855, 2404, 3034, 3909, 4946, 6325, 7997, 10202, 12840, 16328, 20549, 25989, 32627, 41180, 51577, 64872, 81128, 101729, 127016, 158913, 197981, 247163, 307523, 383019

Offset: 0

Author

Ilya Gutkovskiy, Sep 03 2018

Keywords

• nonn

Crossrefs

Cf. A193197, A206100, A206138, A318770.

Programs

Maple

a:=series(add(x^(k^2)/mul((1-x^j)^j,j=1..k),k=0..100),x=0,53): seq(coeff(a,x,n),n=0..52); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 52; CoefficientList[Series[Sum[x^k^2/Product[(1 - x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]