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%I #20 Dec 13 2017 02:45:58
%S 1,8,248,1952,7928,25008,60512,134464,253688,474344,775248,1288416,
%T 1934432,2970352,4168384,6101952,8118008,11358864,14704664,19808800,
%U 24782928,32809216,39940896,51490752,61899872,78150008,92080912
%N Average theta series of odd unimodular lattices in dimension 12.
%D R. A. Rankin, Modular Forms, p. 240 ff.
%D E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 121.
%H G. C. Greubel, <a href="/A029751/b029751.txt">Table of n, a(n) for n = 0..5000</a>
%F G.f.: 1 + 8*Sum_{k>0} k^5 x^k/(1+(-x)^k). - _Michael Somos_, Sep 21 2005
%F A000145(n) = a(n) + 16*A000735(n). - _Michael Somos_, Sep 21 2005
%t a[0] = 1; a[n_] := (-1)^(n-1)*8*DivisorSum[n, (-1)^(n + n/#)*#^5&]; Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Jul 06 2017, translated from PARI *)
%o (PARI) a(n)=if(n<1, n==0, (-1)^(n-1)*8*sumdiv(n,d,(-1)^(n+n/d)*d^5)) /* _Michael Somos_, Sep 21 2005 */
%Y Cf. A000145, A000735.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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