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A376853
G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.
3
1, 1, 4, 9, 16, 28, 49, 84, 140, 228, 361, 560, 856, 1288, 1916, 2821, 4108, 5928, 8480, 12024, 16920, 23637, 32788, 45196, 61928, 84368, 114332, 154160, 206857, 276308, 367476, 486680, 641996, 843656, 1104592, 1441168, 1873965, 2428816, 3138132, 4042408, 5192132
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * exp(sqrt(8*n*(log(r)^2 + polylog(2,r) - polylog(2,-r)))), where r = A192918 = 0.54368901269207636157... is the real root of the equation r*(1+r^2) = (1-r^2) and c = 0.0643033662740307713580663125340126524175...
MATHEMATICA
nmax = 60; CoefficientList[Series[Sum[x^(k*(k+1)/2) * Product[(1+x^j)/(1-x^j), {j, 1, k}]^2, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 06 2024
STATUS
approved