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A029817
Average theta series of odd unimodular lattices of dimension 16 (multiplied by 17).
0
17, 32, 4064, 70016, 528352, 2500032, 8892032, 26353408, 67637216, 153125024, 317504064, 623589504, 1156034176, 2007952576, 3346882816, 5470070016, 8657571808, 13130837568, 19446878048, 28603895680
OFFSET
0,1
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved