A008691 Theta series of Niemeier lattice of type A_17 E_7.

1, 432, 186192, 16881984, 397398096, 4631467680, 34415043264, 187482701952, 814916270160, 2975502394224, 9486501222240, 27053176872384, 70486076751552, 169930845743904, 384163759953792, 820167146628480, 1668890516764752, 3249628128869472, 6096883839494544

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also the theta series for the Niemeier lattice of type D_10 E_7^2. - clarified by Ben Mares, Jul 17 2022

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004009, A013973.

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 = 5/6 E4[q]^3 + 1/6 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 5/6 E_4(z)^3 + 1/6 E_6(z)^2. See A004009 and A013973. - Daniel D. Briggs, Nov 25 2011

Extensions

More terms from Sean A. Irvine, Mar 22 2020