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^j)^2 * x^j.
a(n) ~ c * A376815^sqrt(n) / sqrt(n), where c = 1/(4*sqrt(3/2 - 2*sinh(arcsinh(3^(3/2)/2)/3)/sqrt(3))) = 0.27647151570071656262813536...
MATHEMATICA
nmax = 100; CoefficientList[Series[Sum[x^(n*(n+1)/2)*Product[1+x^k, {k, 1, n}]^2, {n, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^k)*(1 + x^k)*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, Oct 05 2024
STATUS
approved