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A303905
Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(k*(k+1)/2)).
0
1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 9, 10, 10, 11, 12, 13, 15, 16, 17, 19, 20, 22, 24, 24, 26, 29, 30, 31, 34, 36, 37, 41, 44, 44, 47, 50, 52, 56, 59, 62, 65, 67, 70, 73, 75, 79, 85, 89, 91, 96, 100, 102, 108, 113, 116, 123, 129, 132, 137, 142, 147, 153, 158, 162, 169, 176, 182, 190, 196, 201
OFFSET
0,2
COMMENTS
Partial sums of A024940.
FORMULA
a(n) ~ exp(3 * Pi^(1/3) * ((sqrt(2) - 1) * Zeta(3/2))^(2/3) * n^(1/3) / 2^(4/3)) / (2^(1/3) * (sqrt(2) - 1)^(1/3) * sqrt(3) * Pi^(2/3) * Zeta(3/2)^(1/3) * n^(1/6)). - Vaclav Kotesovec, May 04 2018
MATHEMATICA
nmax = 69; CoefficientList[Series[1/(1 - x) Product[1 + x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 02 2018
STATUS
approved