A047805 Duplicate of A008695.

1, 288, 189648, 16845696, 397610064, 4630772160, 34415914176, 187485113088, 814904105040, 2975518758816, 9486517914720, 27053099888256, 70486130167488, 169930928938176, 384163702086528

Offset: 0

Author

N. J. A. Sloane

Keywords

• dead

Comments

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

Crossrefs

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

Programs

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-François Alcover, Jul 06 2017 *)

Formula

This series is the q-expansion of 3/4 E_4(z)^3 + 1/4 E_6(z)^2. Cf. A004009, A013973.

Extensions

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