A191659 First differences of A000219.

0, 2, 3, 7, 11, 24, 38, 74, 122, 218, 359, 620, 1006, 1682, 2712, 4418, 7037, 11267, 17729, 27948, 43516, 67681, 104308, 160411, 244839, 372712, 563913, 850576, 1276378, 1909351, 2843346, 4221120, 6241544, 9200982, 13515091, 19793915, 28894823, 42062211, 61045506, 88359422, 127537058, 183617286, 263666228, 377696338, 539715276, 769456793

Offset: 0

Author

N. J. A. Sloane, Jun 10 2011

Keywords

• nonn

References

• G. Almkvist, The differences of the number of plane partitions, Manuscript, circa 1991.

Crossrefs

Cf. A000219, A191660, A191661.

Programs

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[1/(1 - x^k)^k, {k, 2, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Oct 05 2015 *)

Formula

a(n) ~ 2^(1/36) * Zeta(3)^(19/36) * exp(1/12 + 3*Zeta(3)^(1/3)*n^(2/3)/2^(2/3)) / (A * sqrt(3*Pi) * n^(37/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Oct 05 2015