The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A028977 Theta series of 8-d 6-modular lattice G_2 tensor F_4 (or A_2 tensor D_4) with det 1296 and minimal norm 4 in powers of q^2. 2
 1, 0, 72, 192, 504, 576, 2280, 1728, 4248, 4800, 7920, 6336, 19416, 10368, 21312, 22464, 33624, 24192, 63048, 32832, 65808, 60864, 83232, 57600, 155640, 76032, 137520, 130944, 180288, 116928, 290736 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Proposition 7.6 [McKay and Sebbar, 2000, p. 272, equ. (7.8)] expresses the theta series as a Schwarzian of A007258 and tau. - Michael Somos, Jun 05 2015 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275. G. Nebe and N. J. A. Sloane, Home page for this lattice E. M. Rains and N. J. A. Sloane, The Shadow Theory of Modular and Unimodular Lattices, J. Number Theory, 73 (1998), 359-389. FORMULA Expansion of ((eta(q^2) * eta(q^3))^7 / (eta(q) * eta(q^6))^5 - (eta(q) * eta(q^6))^7 / (eta(q^2) * eta(q^3))^5)^2 - 8 * (eta(q^2) * eta(q^4) * eta(q^6) * eta(q^12))^2 in powers of q. - Michael Somos, May 27 2012 A212817(n) = a(n) + 8 * A030209(n). - Michael Somos, May 27 2012 G.f. A(x) = g1(x)^2 * (1 - 4*g2(x) - 16*g2(x)^3 + 16*g2(x)^4) where g1(x) = A033712(x) and g2(x) = A212770(x). - Michael Somos, Apr 19 2015 EXAMPLE G.f. = 1 + 72*x^2 + 192*x^3 + 504*x^4 + 576*x^5 + 2280*x^6 + 1728*x^7 + ... G.f. = 1 + 72*q^4 + 192*q^6 + 504*q^8 + 576*q^10 + 2280*q^12 + 1728*q^14 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ With[{e1 = QPochhammer[ x] QPochhammer[ x^6], e2 = QPochhammer[ x^2] QPochhammer[ x^3]}, (e2^7 / e1^5 - x e1^7 /e2^5)^2 - 8 x (e1 e2)^2], {x, 0, n}]; (* Michael Somos, Apr 19 2015 *) PROG (PARI) {a(n) = local(A, B); if( n<0, 0, A = x * O(x^n); B = eta(x^2 + A) * eta(x^3 + A); A = eta(x + A) * eta(x^6 + A); polcoeff( (B^7 / A^5 - x * A^7 / B^5)^2 - 8 * x * (A * B)^2, n))}; /* Michael Somos, May 27 2012 */ (Magma) A := Basis( ModularForms( Gamma0(6), 4), 32); A[1] + 72*A[3] + 192*A[4] + 504*A[5]; /* Michael Somos, Aug 20 2014 */ CROSSREFS Cf. A007258, A030209, A033712, A212770, A212817. Sequence in context: A044785 A254437 A304376 * A033693 A250786 A302886 Adjacent sequences: A028974 A028975 A028976 * A028978 A028979 A028980 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 23:40 EDT 2023. Contains 361623 sequences. (Running on oeis4.)