A376852 G.f.: Sum_{k>=0} x^(k*(k+1)) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.
1, 0, 1, 4, 8, 12, 17, 24, 36, 56, 88, 136, 205, 300, 428, 600, 828, 1132, 1540, 2084, 2813, 3788, 5080, 6788, 9032, 11952, 15736, 20612, 26852, 34812, 44929, 57732, 73900, 94268, 119852, 151932, 192072, 242172, 304584, 382164, 478364, 597400, 744365, 925384
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
nmax = 60; CoefficientList[Series[Sum[x^(k*(k+1)) * Product[(1+x^j)/(1-x^j), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(Pi*sqrt(n)) / (2^(9/2) * n).