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A008695 Theta series of Niemeier lattice of type A_11 D_7 E_6. 2
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

REFERENCES

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

LINKS

Table of n, a(n) for n=0..14.

FORMULA

This series is the q-expansion of 3/4 E_4(z)^3 + 1/4 E_6(z)^2. Cf. A004009, A013973. - 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-Fran├žois Alcover, Jul 05 2017 *)

CROSSREFS

Equal to theta series of E_6^4, cf. A047805.

Sequence in context: A037946 A282102 A159299 * A047805 A173150 A282332

Adjacent sequences:  A008692 A008693 A008694 * A008696 A008697 A008698

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)