OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: exp(Sum_{k>=1} (-1)^k*x^k*(2 - x^k)/(k*(1 - x^k)^2)).
a(n) ~ (-1)^n * exp(3 * Zeta(3)^(1/3) * n^(2/3) / 2^(5/3) + Pi^2 * n^(1/3) / (3 * 2^(7/3) * Zeta(3)^(1/3)) - 1/12 - Pi^4 / (864 * Zeta(3))) * A * Zeta(3)^(5/36) / (2^(7/9) * sqrt(3*Pi) * n^(23/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Aug 21 2018
MATHEMATICA
nmax = 48; CoefficientList[Series[Product[1/(1 + x^k)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 48; CoefficientList[Series[Exp[Sum[(-1)^k x^k (2 - x^k)/(k (1 - x^k)^2), {k, 1, nmax}]], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d) d (d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 48}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 11 2018
STATUS
approved