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, 41278028352, 57661256704, 79195867008, 108954414336, 147990228608

Offset

0,1

Links

Table of n, a(n) for n=0..24.

Heng Huat Chan and Christian Krattenthaler, Recent progress in the study of representations of integers as sums of squares, Bulletin of the London Mathematical Society, Vol. 37, No. 6 (2005), pp. 818-826; arXiv preprint, arXiv:math/0407061 [math.NT], 2004.

Formula

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

a(n) = 32 * (-1)^n * (A013955(n) - 2 * A321811(2*n)) for n >= 1. - Amiram Eldar, Jan 07 2025

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, A321811.

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