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A023924 Theta series of A*_12 lattice. 0
1, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 156, 0, 156, 0, 572, 0, 0, 1430, 1716, 2574, 3432, 0, 0, 5746, 0, 4290, 0, 13182, 0, 0, 22308, 26052, 29744, 33462, 0, 0, 54912, 0, 36036, 0, 89232, 0, 0, 123708, 143000, 156156, 178464, 0, 0, 234234, 0, 141726, 0, 348374, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.
LINKS
Kok Seng Chua, Circular Summation of the 13th powers of Ramanujan Theta Functions, Ramanujan J., 5 (2001), 353-354.
FORMULA
G.f.: y^13/x + 13*x*y^11 + 78*x^3*y^9 + 260*x^5*y^7 + 494*x^7*y^5 + 468*x^9*y^3 + 169*x^11*y + 13*x^13/y where x=eta(13z) and y=eta(z).
EXAMPLE
1 + 26*q^6 + 156*q^11 + 156*q^13 + 572*q^15 + 1430*q^18 + 1716*q^19 + ...
MATHEMATICA
a[n_] := Module[{A, B}, A = x*O[x]^n; B = x*(QPochhammer[x^13 + A] / QPochhammer[x + A])^2; SeriesCoefficient[(QPochhammer[x + A]^13 / QPochhammer[x^13 + A])*(1 + 13*B*(1 + 6*B + 20*B^2 + 38*B^3 + 36*B^4 + 13*B^5 + B^6)), {x, 0, n}]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Nov 05 2015, translated from PARI *)
PROG
(PARI) {a(n) = local(A, B); if( n<0, 0, A = x * O(x^n); B = x * (eta(x^13 + A) / eta(x + A))^2; polcoeff( eta(x + A)^13 / eta(x^13 + A) * (1 + 13*B * (1 + 6*B + 20*B^2 + 38*B^3 + 36*B^4 + 13*B^5 + B^6)), n))} /* Michael Somos, Jun 24 2013 */
CROSSREFS
Sequence in context: A237522 A347810 A116197 * A022066 A291551 A217232
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 31 2001
STATUS
approved

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Last modified June 24 09:30 EDT 2024. Contains 373674 sequences. (Running on oeis4.)