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A008700 Theta series of Niemeier lattice of type D_4^6. 5
1, 144, 193104, 16809408, 397822032, 4630076640, 34416785088, 187487524224, 814891939920, 2975535123408, 9486534607200, 27053022904128, 70486183583424, 169931012132448, 384163644219264, 820166796086400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the theta series of A_5^4*D_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 (2*E_4(z)^3 + E_6(z)^2)/3. - 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[ (2/3)*E4^3 + (1/3)*E6^2 + O[q]^terms, q] (* Jean-Fran├žois Alcover, Jul 05 2017 *)

CROSSREFS

Cf. A004009, A013973.

Cf. A008688 - A008699, A008701, A008702, A008703, A008704.

Sequence in context: A203098 A159724 A221124 * A047807 A023112 A159424

Adjacent sequences:  A008697 A008698 A008699 * A008701 A008702 A008703

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 24 18:12 EDT 2022. Contains 354043 sequences. (Running on oeis4.)