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

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, A191659, A191661.

Programs

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 *)

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