A284830 Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).
1, 2, 3, 5, 6, 8, 10, 14, 16, 19, 23, 30, 33, 38, 44, 55, 60, 69, 77, 93, 102, 113, 126, 148, 162, 177, 198, 226, 246, 268, 293, 334, 361, 392, 424, 480, 516, 556, 601, 668, 721, 773, 835, 917, 990, 1054, 1129, 1239, 1325, 1415, 1508, 1649, 1757, 1875, 1990, 2157, 2303, 2441, 2595, 2796
Offset: 1
Keywords
Examples
a(9) = 16 because we have [9], [4, 4, 1], [4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 1 + 5 + 9 = 16.
Programs
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Mathematica
nmax = 60; Rest[CoefficientList[Series[Sum[x^i^2/(1 - x^i^2) Product[1/(1 - x^j^2), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]] -
PARI
x='x+O('x^61); Vec(sum(i=1, 60, x^i^2/(1 - x^i^2) * prod(j=i, 60, 1/(1 - x^j^2)))) \\ Indranil Ghosh, Apr 04 2017
Formula
G.f.: Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).
Comments