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A212817 Theta series of direct sum of 2 copies of 4-dimensional lattice QQF.4.i. 2
1, 8, 56, 168, 536, 624, 2328, 1600, 4184, 4872, 7824, 6432, 19320, 10672, 21568, 22320, 33752, 23184, 62904, 32992, 66000, 61248, 83040, 58944, 155832, 75320, 136912, 130728, 179776, 117168, 291024, 142720, 269528, 236448, 307440, 207744, 528024, 243952 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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 in powers of q.

G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 576 (t/i)^4 f(t) where q = exp(2 Pi i t).

Convolution square of A125514.

a(n) = A028977(n) + 8 * A030209(n). - Michael Somos, Jun 05 2015

EXAMPLE

G.f. = 1 + 8*x + 56*x^2 + 168*x^3 + 536*x^4 + 624*x^5 + 2328*x^6 + 1600*x^7 + ...

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 ], {x, 0, n}]; (* Michael Somos, Apr 19 2015 *)

PROG

(PARI) {a(n) = my(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, n))};

(PARI) {a(n) = my(G); if( n<0, 0, G = [ 2, 0, 1, 1; 0, 2, 1, 1; 1, 1, 4, 1; 1, 1, 1, 4 ]; polcoeff( (1 + 2 * x * Ser( qfrep( G, n, 1)))^2, n))};

(MAGMA) A := Basis( ModularForms( Gamma0(6), 4), 38); A[1] + 8*A[2] + 56*A[3] + 168*A[4] + 536*A[5]; /* Michael Somos, Jun 04 2015 */

CROSSREFS

Cf. A028977, A030209, A125514.

Sequence in context: A003722 A044146 A118772 * A267522 A073831 A168013

Adjacent sequences:  A212814 A212815 A212816 * A212818 A212819 A212820

KEYWORD

nonn

AUTHOR

Michael Somos, May 27 2012

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)