A008689 Theta series of Niemeier lattice of type A_24.

1, 600, 182160, 16924320, 397150800, 4632279120, 34414027200, 187479888960, 814930462800, 2975483302200, 9486481747680, 27053266687200, 70486014432960, 169930748683920, 384163827465600

Offset

0,2

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = A023936(25n). - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Aug 02 2001

This series is the q-expansion of 67/72 E_4(z)^3 + 5/72 E_6(z)^2. - Daniel D. Briggs, Nov 25 2011

Mathematica

terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 67/72 E4[q]^3 + 5/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Crossrefs

Cf. A004009, A013973, A023936.

Sequence in context: A023915 A035850 A093260 * A126835 A020370 A325089

Adjacent sequences: A008686 A008687 A008688 * A008690 A008691 A008692

Keyword

nonn

Author

N. J. A. Sloane

Status

approved