A306706 Expansion of Sum_{k>=0} x^(k*(k+1)/2) / Product_{j=1..k} (1 + x^j)^j.

1, 1, -1, 2, -2, 0, 1, 2, -4, -3, 7, 4, -4, -14, 6, 10, 12, -14, 0, -26, 3, 7, 60, 11, -27, -99, -26, 6, 126, 94, 58, -87, -180, -201, -46, 145, 282, 330, 142, -21, -515, -573, -716, -15, 423, 1519, 1128, 1197, -783, -1378, -3264, -1892, -1574, 2155, 2679, 6075, 3376, 3243

Offset: 0

Author

Ilya Gutkovskiy, Mar 05 2019

Keywords

• sign

Crossrefs

Cf. A003406, A206138.

Programs

Mathematica

nmax = 57; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 + x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]