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A008704 Theta series of Niemeier lattice of type A_1^24. 1
1, 48, 195408, 16785216, 397963344, 4629612960, 34417365696, 187489131648, 814883829840, 2975546033136, 9486545735520, 27052971581376, 70486219194048, 169931067595296, 384163605641088 (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 11/18*E_4(z)^3 + 7/18*E_6(z)^2. Cf. A004009, A013973. - Daniel D. Briggs, Nov 26 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 = 11/18 E4[q]^3 + 7/18 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: A081262 A238001 A228143 * A037947 A282596 A272262

Adjacent sequences:  A008701 A008702 A008703 * A008705 A008706 A008707

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)