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A034950
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Expansion of eta(8z)*eta(16z)*theta_3(2z).
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1
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1, 2, 0, 0, 1, -2, 0, 0, -4, -2, 0, 0, -3, 0, 0, 0, 4, -4, 0, 0, 0, 6, 0, 0, 1, 4, 0, 0, 4, 2, 0, 0, 0, -2, 0, 0, 4, -2, 0, 0, -3, 2, 0, 0, -4, -4, 0, 0, -4, 2, 0, 0, -8, -6, 0, 0, 8, -4, 0, 0, 1, -4, 0, 0, -4, 6, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 4, 8, 0, 0, 0, 6, 0, 0, 5, -2, 0, 0, 4, -2, 0, 0, 8, 4, 0, 0, -4, -8, 0, 0, -4, 8, 0, 0, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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REFERENCES
| Ono and Skinner, Ann. Math., 147 (1998), 453-470.
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Euler transform of period 8 sequence [2,-3,2,-2,2,-3,2,-3,...]. - Michael Somos Feb 16 2006
Expansion of q^(-1/2)eta(q^2)^5*eta(q^8)/(eta(q)^2*eta(q^4)) in powers of q. - Michael Somos Feb 16 2006
Expansion of phi(q)psi(q^4)phi(-q^4) in powers of q where phi(),psi() are Ramanujan theta functions.
G.f.: Product_{k>0} (1+x^k)^2*(1-x^(2k))^3*(1+x^(4k)) . - Michael Somos Feb 16 2006
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EXAMPLE
| q+2*q^3+1*q^9-2*q^11-4*q^17-2*q^19-...
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^5*eta(x^8+A)/(eta(x+A)^2*eta(x^4+A)), n))} /* Michael Somos Feb 16 2006 */
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CROSSREFS
| A080963(2n+1)=2*a(n).
Sequence in context: A023555 A143377 A143380 * A099584 A100563 A087773
Adjacent sequences: A034947 A034948 A034949 * A034951 A034952 A034953
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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