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A008703 Theta series of Niemeier lattice of type A_2^12. 1
1, 72, 194832, 16791264, 397928016, 4629728880, 34417220544, 187488729792, 814885857360, 2975543305704, 9486542953440, 27052984412064, 70486210291392, 169931053729584, 384163615285632 (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 5/8 E_4(z)^3 + 3/8 E_6(z)^2. Cf. A004009, A013973. - 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 = 5/8 E4[q]^3 + 3/8 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-Fran├žois Alcover, Jul 06 2017 *)

CROSSREFS

Sequence in context: A279656 A318184 A290182 * A135320 A135427 A028671

Adjacent sequences:  A008700 A008701 A008702 * A008704 A008705 A008706

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)