A191660 Second differences of A000219.

2, 1, 4, 4, 13, 14, 36, 48, 96, 141, 261, 386, 676, 1030, 1706, 2619, 4230, 6462, 10219, 15568, 24165, 36627, 56103, 84428, 127873, 191201, 286663, 425802, 632973, 933995, 1377774, 2020424, 2959438, 4314109, 6278824, 9100908, 13167388, 18983295, 27313916, 39177636, 56080228, 80048942, 114030110, 162018938, 229741517, 325000341, 458854803, 646409612

Offset

0,1

References

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

Links

Table of n, a(n) for n=0..47.

Formula

a(n) ~ 2^(13/36) * Zeta(3)^(31/36) * exp(1/12 + 3*Zeta(3)^(1/3)*n^(2/3)/2^(2/3)) / (A * sqrt(3*Pi) * n^(49/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Oct 30 2016

Mathematica

Differences[CoefficientList[Series[Product[(1-x^k)^-k, {k, 1, 64}], {x, 0, 64}], x], 2] (* Harvey P. Dale, Jun 19 2011 *)
nmax = 50; Drop[CoefficientList[Series[(1-x)^2 * Product[1/(1-x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x], 2] (* Vaclav Kotesovec, Oct 30 2016 *)

Crossrefs

Cf. A000219, A191659, A191661.

Sequence in context: A212716 A057772 A145861 * A129874 A021983 A349994

Adjacent sequences: A191657 A191658 A191659 * A191661 A191662 A191663

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2011

Status

approved