login
First differences of A000219.
11

%I #10 Oct 05 2015 08:52:53

%S 0,2,3,7,11,24,38,74,122,218,359,620,1006,1682,2712,4418,7037,11267,

%T 17729,27948,43516,67681,104308,160411,244839,372712,563913,850576,

%U 1276378,1909351,2843346,4221120,6241544,9200982,13515091,19793915,28894823,42062211,61045506,88359422,127537058,183617286,263666228,377696338,539715276,769456793

%N First differences of A000219.

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

%F 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

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

%Y Cf. A000219, A191660, A191661.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 10 2011