The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008695 Theta series of Niemeier lattice of type A_11 D_7 E_6. 5
 1, 288, 189648, 16845696, 397610064, 4630772160, 34415914176, 187485113088, 814904105040, 2975518758816, 9486517914720, 27053099888256, 70486130167488, 169930928938176, 384163702086528 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the theta series of E_6^4. 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 This series is the q-expansion of (3*E_4(z)^3 + E_6(z)^2)/4. - Daniel D. Briggs, Nov 25 2011 MATHEMATICA terms = 15; th = EllipticTheta; E4 = 1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}] + O[q]^terms; E6 = th[2, 0, q]^12 + th[3, 0, q]^12 - 33*th[2, 0, q]^4*th[3, 0, q]^4*(th[2, 0, q]^4 + th[3, 0, q]^4); CoefficientList[ (3/4)*E4^3 + (1/4)*E6^2 + O[q]^terms, q] (* Jean-François Alcover, Jul 05 2017 *) CROSSREFS Cf. A004009, A013973. Cf. A008688 - A008694, A008696 - A008704. Sequence in context: A037946 A282102 A159299 * A047805 A173150 A282332 Adjacent sequences:  A008692 A008693 A008694 * A008696 A008697 A008698 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 29 06:21 EDT 2021. Contains 346340 sequences. (Running on oeis4.)