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A304631
Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(2*k-1)).
2
1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 18, 21, 24, 28, 33, 38, 43, 49, 56, 64, 72, 81, 92, 104, 116, 130, 146, 163, 181, 201, 224, 249, 275, 304, 337, 372, 409, 450, 496, 545, 597, 654, 717, 785, 857, 935, 1022, 1115, 1213, 1320, 1437, 1562, 1695, 1839, 1996, 2164, 2342, 2534
OFFSET
0,2
COMMENTS
Partial sums of A000700.
FORMULA
G.f.: (1/(1 - x))*Product_{k>=1} 1/(1 + (-x)^k).
a(n) ~ exp(Pi*sqrt(n/6)) * 3^(1/4) / (Pi * 2^(1/4) * n^(1/4)). - Vaclav Kotesovec, May 19 2018
MATHEMATICA
nmax = 59; CoefficientList[Series[1/(1 - x) Product[(1 + x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 59; CoefficientList[Series[1/(1 - x) Product[1/(1 + (-x)^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 15 2018
STATUS
approved