A029751 Average theta series of odd unimodular lattices in dimension 12.

1, 8, 248, 1952, 7928, 25008, 60512, 134464, 253688, 474344, 775248, 1288416, 1934432, 2970352, 4168384, 6101952, 8118008, 11358864, 14704664, 19808800, 24782928, 32809216, 39940896, 51490752, 61899872, 78150008, 92080912

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• R. A. Rankin, Modular Forms, p. 240 ff.
• E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 121.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000145, A000735.

Programs

Mathematica

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 *)

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 */

Formula

G.f.: 1 + 8*Sum_{k>0} k^5 x^k/(1+(-x)^k). - Michael Somos, Sep 21 2005

A000145(n) = a(n) + 16*A000735(n). - Michael Somos, Sep 21 2005