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A047805 Duplicate of A008695. 0
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

COMMENTS

Original title: Theta series of Niemeier lattice of type E_6^4.

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.

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 = 3/4 E4[q]^3 + 1/4 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-Fran├žois Alcover, Jul 06 2017 *)

CROSSREFS

Equal to theta series of A_11 D_7 E_6, cf. A008695

Sequence in context: A282102 A159299 A008695 * A173150 A282332 A291187

Adjacent sequences:  A047802 A047803 A047804 * A047806 A047807 A047808

KEYWORD

nonn,dead

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms and formula in terms of Eisenstein series from Daniel D. Briggs, Nov 25 2011

STATUS

approved

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Last modified April 12 01:36 EDT 2021. Contains 342912 sequences. (Running on oeis4.)