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A003785
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Coefficients of Jacobi cusp form of index 1 and weight 12.
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1
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1, 10, 0, 0, -88, -132, 0, 0, 1275, 736, 0, 0, -8040, -2880, 0, 0, 24035, 13080, 0, 0, -14136, -54120, 0, 0, -128844, 115456, 0, 0, 389520, 38016, 0, 0, -256410, -697950, 0, 0, -806520, 963160, 0, 0, 1892363, 938400, 0, 0, -1227600, -2309120, 0, 0, -813450, -2813096, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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REFERENCES
| M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 141.
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FORMULA
| (theta_3(z)^4+(theta_2(z)^4)/4)*eta(4z)^18*theta_4(z) - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 11 2000
a(4*n+1) = a(4*n+2) = 0.
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EXAMPLE
| q^3 + 10*q^4 - 88*q^7 - 132*q^8 + 1275*q^11 + 736*q^12 - 8040*q^15 - ...
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PROG
| (PARI) {a(n) = local(A, A1); if( n<3, 0, n -= 3; A = x * O(x^n); A1 = (eta(x^2 + A)^3 / eta(x + A) / eta(x^4 + A)^2)^4 ; polcoeff( (A1 + 4 * x / A1) * eta(x^2 + A)^7 * eta(x^4 + A)^18 / eta(x + A)^2, n))} /* Michael Somos Oct 24 2007 */
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CROSSREFS
| Cf. A003784.
Sequence in context: A063699 A167165 A064511 * A038689 A030000 A062520
Adjacent sequences: A003782 A003783 A003784 * A003786 A003787 A003788
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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