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A008698 Theta series of Niemeier lattice of type A_7^2 D_5^2. 4
1, 192, 191952, 16821504, 397751376, 4630308480, 34416494784, 187486720512, 814895994960, 2975529668544, 9486529043040, 27053048565504, 70486165778112, 169930984401024, 384163663508352 (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

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

FORMULA

This series is the q-expansion of (25*E_4(z)^3 + 11*E_6(z)^2)/36. - 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 = 25/36 E4[q]^3 + 11/36 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-Fran├žois Alcover, Jul 06 2017 *)

CROSSREFS

Cf. A004009, A013973.

Cf. A008688 - A008697, A008699 - A008704.

Sequence in context: A183701 A208795 A203490 * A282541 A202930 A300848

Adjacent sequences:  A008695 A008696 A008697 * A008699 A008700 A008701

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)