A008690 -id:A008690 - cp's OEIS frontend

A008692 Theta series of Niemeier lattice of type A_15 D_9.

1, 384, 187344, 16869888, 397468752, 4631235840, 34415333568, 187483505664, 814912215120, 2975507849088, 9486506786400, 27053151211008, 70486094556864, 169930873475328, 384163740664704

Offset: 0

N. J. A. Sloane

nonn

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

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

Cf. A008688, A008689, A008690, A008691, A008693 - A008704.

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 = 29/36 E4[q]^3 + 7/36 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

This series is the q-expansion of (29*E_4(z)^3 + 7*E_6(z)^2)/36. See A004009 and A013973. - Daniel D. Briggs, Nov 25 2011

A055750 Jacobi form of weight 12 and index 1 for the Niemeier lattice of type D_12^2.

Original entry on oeis.org

1, 0, 0, 40, 446, 0, 0, 28864, 125268, 0, 0, 3725112, 9205336, 0, 0, 95337792, 188112798, 0, 0, 1143987064, 1960280520, 0, 0, 8506064832, 13290845832, 0, 0, 45757418528, 67078180928, 0, 0, 195405086592, 272569432212, 0, 0

Offset: 0

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 12 2000

nonn

A008690, A055749, A003785.

E_8*E_{4, 1}-16*phi_12.

G.f.: b(z) - 16*c(z) where b(z) is the g.f. for A055747 and c(z) is the g.f. for A003785. Sean A. Irvine, Apr 05 2022

cp's OEIS Frontend

A008692 Theta series of Niemeier lattice of type A_15 D_9.

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