A072338 EULER transform of A002620 (with the initial 0,0,1 omitted).

1, 2, 7, 18, 48, 114, 273, 614, 1370, 2952, 6275, 13034, 26725, 53854, 107238, 210670, 409446, 786936, 1498147, 2825084, 5282409, 9795620, 18027645, 32935112, 59760481, 107724038, 192984835, 343676216, 608589028, 1071869694, 1878068324, 3274291480, 5681336242

Offset

0,2

Links

Table of n, a(n) for n=0..32.

N. J. A. Sloane, Transforms

Formula

a(n) ~ exp(2*sqrt(2)*Pi*n^(3/4) / (3*15^(1/4)) + 2*Zeta(3) * sqrt(15*n) / Pi^2 + (7*5^(1/4)*Pi / (8*sqrt(2)*3^(3/4)) - 30*sqrt(2) * 15^(1/4) * Zeta(3)^2 /Pi^5) * n^(1/4) + 1200*Zeta(3)^3/Pi^8 - 71*Zeta(3)/(16*Pi^2) + 1/12) * Pi^(1/12) / (4*A * 2^(5/12) * 15^(13/48) * n^(37/48)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, May 31 2019

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1 - x^k)^Floor[(k + 2)^2/4], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 31 2019 *)

Crossrefs

Sequence in context: A247289 A161870 A362126 * A182197 A022726 A192873

Adjacent sequences: A072335 A072336 A072337 * A072339 A072340 A072341

Keyword

nonn

Author

N. J. A. Sloane, Jul 16 2002

Status

approved