A029817 Average theta series of odd unimodular lattices of dimension 16 (multiplied by 17).

17, 32, 4064, 70016, 528352, 2500032, 8892032, 26353408, 67637216, 153125024, 317504064, 623589504, 1156034176, 2007952576, 3346882816, 5470070016, 8657571808, 13130837568, 19446878048, 28603895680

Offset

0,1

Links

Table of n, a(n) for n=0..19.

H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares, arXiv:math/0407061 [math.NT], 2004.

Formula

G.f.: 17 + 32 * Sum_{k >= 1} k^7*q^k/(1-(-q)^k).

Mathematica

max = 20; s = 17 + 32*Sum[k^7*q^k/(1-(-q)^k), {k, 1, max}] + O[q]^max; CoefficientList[s, q] (* Jean-François Alcover, Dec 07 2015 *)

Prog

(PARI) a(n)=if(n<1, 17*(n==0), 32*sumdiv(n, d, d^7-2*if(d%4==2, (d/2)^7))) /* Michael Somos, Jul 16 2004 */

Crossrefs

Cf. A013955.

Sequence in context: A043907 A173054 A162624 * A162504 A336235 A085255

Adjacent sequences: A029814 A029815 A029816 * A029818 A029819 A029820

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved