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

0,2

References

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

Links

Table of n, a(n) for n=0..45.

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

Mathematica

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

Crossrefs

Cf. A000219, A191660, A191661.

Sequence in context: A129940 A128631 A092217 * A007481 A238312 A121268

Adjacent sequences: A191656 A191657 A191658 * A191660 A191661 A191662

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2011

Status

approved