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%I #18 Jan 07 2025 02:37:34
%S 17,32,4064,70016,528352,2500032,8892032,26353408,67637216,153125024,
%T 317504064,623589504,1156034176,2007952576,3346882816,5470070016,
%U 8657571808,13130837568,19446878048,28603895680,41278028352,57661256704,79195867008,108954414336,147990228608
%N Average theta series of odd unimodular lattices of dimension 16 (multiplied by 17).
%H Heng Huat Chan and Christian Krattenthaler, <a href="https://doi.org/10.1112/S0024609305004820">Recent progress in the study of representations of integers as sums of squares</a>, Bulletin of the London Mathematical Society, Vol. 37, No. 6 (2005), pp. 818-826; <a href="https://arxiv.org/abs/math/0407061">arXiv preprint</a>, arXiv:math/0407061 [math.NT], 2004.
%F G.f.: 17 + 32 * Sum_{k >= 1} k^7*q^k/(1-(-q)^k).
%F a(n) = 32 * (-1)^n * (A013955(n) - 2 * A321811(2*n)) for n >= 1. - _Amiram Eldar_, Jan 07 2025
%t 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 *)
%o (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 */
%Y Cf. A013955, A321811.
%K nonn
%O 0,1
%A _N. J. A. Sloane_