login
A376709
G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} 1/(1 - x^j)^3.
1
1, 1, 3, 6, 11, 18, 30, 47, 75, 115, 177, 264, 394, 573, 831, 1184, 1679, 2349, 3273, 4511, 6192, 8428, 11422, 15372, 20606, 27453, 36435, 48103, 63270, 82833, 108068, 140399, 181806, 234541, 301636, 386604, 494080, 629459, 799770, 1013253, 1280463
OFFSET
0,3
FORMULA
a(n) ~ (log(r)^2 + 3*polylog(2, 1-r))^(3/4) * exp(2*sqrt((log(r)^2 + 3*polylog(2, 1-r))*n)) / (4 * Pi^(3/2) * r^(2/3) * sqrt(2+r) * n^(5/4)), where r = 1 - A357471 = 0.4301597090019467340886... is the real root of the equation r^2 = (1-r)^3.
MATHEMATICA
nmax = 40; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^j, {j, 1, k}]^3, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 02 2024
STATUS
approved