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A029751 Average theta series of odd unimodular lattices in dimension 12. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

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

MATHEMATICA

a[0] = 1; a[n_] := (-1)^(n-1)*8*DivisorSum[n, (-1)^(n + n/#)*#^5&]; Table[a[n], {n, 0, 26}] (* Jean-Fran├žois Alcover, Jul 06 2017, translated from PARI *)

PROG

(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 */

CROSSREFS

Cf. A000145, A000735.

Sequence in context: A316802 A299648 A219269 * A035036 A221518 A317519

Adjacent sequences:  A029748 A029749 A029750 * A029752 A029753 A029754

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 23 16:19 EST 2020. Contains 332176 sequences. (Running on oeis4.)