OFFSET
0,2
COMMENTS
From Vaclav Kotesovec, Oct 30 2016: (Start)
More generally, for fixed m > 0, if a(m,n) are m-fold differences of A000219, then
a(m,n) ~ A000219(n) * (2*Zeta[3]/n)^(m/3).
a(m,n) ~ Zeta(3)^(7/36 + m/3) * exp(3 * Zeta(3)^(1/3) * (n/2)^(2/3) + 1/12) / (A * sqrt(3*Pi) * 2^(11/36 - m/3) * n^(25/36 + m/3)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
(End)
REFERENCES
G. Almkvist, The differences of the number of plane partitions, Manuscript, circa 1991.
FORMULA
a(n) ~ 2^(25/36) * Zeta(3)^(43/36) * exp(1/12 + 3*Zeta(3)^(1/3)*n^(2/3)/2^(2/3)) / (A * sqrt(3*Pi) * n^(61/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Oct 30 2016
MATHEMATICA
nmax = 50; Drop[CoefficientList[Series[(1-x)^3 * Product[1/(1-x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x], 3] (* Vaclav Kotesovec, Oct 30 2016 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Jun 10 2011
STATUS
approved