A334626 G.f.: Sum_{k>=0} x^(k^3) / Product_{j=1..k^3} (1 - x^j).
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 16, 23, 30, 41, 53, 71, 90, 117, 147, 187, 231, 289, 354, 436, 528, 642, 770, 927, 1102, 1313, 1550, 1832, 2147, 2519, 2935, 3421, 3964, 4594, 5298, 6110, 7016, 8055, 9216, 10542, 12021, 13706, 15588, 17724, 20111
Offset: 0
Keywords
Examples
a(10) = 3 because we have [10], [3, 1, 1, 1, 1, 1, 1, 1] and [2, 2, 1, 1, 1, 1, 1, 1] (see the first comment) or [8, 2], [8, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the second comment).
Programs
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Mathematica
nmax = 53; CoefficientList[Series[Sum[x^(k^3)/Product[1 - x^j, {j, 1, k^3}], {k, 0, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x]
Comments