Original entry on oeis.org
1, 288, 189648, 16845696, 397610064, 4630772160, 34415914176, 187485113088, 814904105040, 2975518758816, 9486517914720, 27053099888256, 70486130167488, 169930928938176, 384163702086528
Offset: 0
Equal to theta series of A_11 D_7 E_6, cf.
A008695
-
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 *)
More terms and formula in terms of Eisenstein series from
Daniel D. Briggs, Nov 25 2011
A008696
Theta series of Niemeier lattice of type D_6^4.
Original entry on oeis.org
1, 240, 190800, 16833600, 397680720, 4630540320, 34416204480, 187485916800, 814900050000, 2975524213680, 9486523478880, 27053074226880, 70486147972800, 169930956669600, 384163682797440, 820166912933760
Offset: 0
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
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terms = 15; th = EllipticTheta; E4 = 1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}] + O[q]^terms; E6 = th[2, 0, q]^12 + th[3, 0, q]^12 - 33*th[2, 0, q]^4*th[3, 0, q]^4*(th[2, 0, q]^4 + th[3, 0, q]^4); CoefficientList[ (13/18)*E4^3 + (5/18)*E6^2 + O[q]^terms, q] (* Jean-François Alcover, Jul 05 2017 *)
A008694
Theta series of Niemeier lattice of type A_12^2.
Original entry on oeis.org
1, 312, 189072, 16851744, 397574736, 4630888080, 34415769024, 187484711232, 814906132560, 2975516031384, 9486515132640, 27053112718944, 70486121264832, 169930915072464, 384163711731072
Offset: 0
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
-
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 = 55/72 E4[q]^3 + 17/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)
A055757
Jacobi form of weight 12 and index 1 for Niemeier lattice of type E_6^4 or A_11 D_7 E_6.
Original entry on oeis.org
1, 0, 0, 20, 246, 0, 0, 30624, 127908, 0, 0, 3699612, 9190616, 0, 0, 95498592, 188170398, 0, 0, 1143506364, 1960018920, 0, 0, 8506347552, 13291928232, 0, 0, 45759995408, 67075871808, 0, 0, 195397296192, 272568671892, 0, 0
Offset: 0
Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 12 2000
- Eichler and Zagier, The Theory of Jacobi Forms, Birkhauser,1985.
Showing 1-4 of 4 results.
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