OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Sum_{k>=0} Product_{j=1..k} (1 + x^(2*j-1))^2 * x^j.
a(n) ~ c * A376659^sqrt(n) / sqrt(n), where c = sqrt(1/14 + sinh(arcsinh(75*sqrt(69)/2)/3)/(7*sqrt(69))) = 0.3792934340515155206194952273079851598271882968396...
MATHEMATICA
nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j-1), {j, 1, k}]^2, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*(1 + x^(2*k - 1))*x^k]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p; , {k, 1, Sqrt[2*nmax]}]; Take[CoefficientList[s, x], nmax + 1]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 30 2024
STATUS
approved