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A123884
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Expansion of phi(q)phi(q^6)/chi(-q^2) in powers of q where phi(),chi() are Ramanujan theta functions.
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7
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1, 2, 1, 2, 3, 2, 2, 0, 2, 2, 1, 4, 0, 2, 3, 2, 2, 0, 4, 2, 2, 0, 0, 2, 1, 4, 2, 2, 2, 2, 3, 2, 0, 2, 2, 2, 2, 0, 2, 4, 4, 0, 0, 0, 1, 2, 4, 0, 2, 4, 2, 2, 1, 6, 0, 2, 2, 0, 0, 2, 4, 2, 0, 2, 2, 0, 4, 0, 4, 2, 1, 2, 0, 2, 4, 0, 0, 2, 2, 4, 3, 4, 0, 2, 2, 2, 2, 0, 4, 2, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 2, 2, 3, 2, 2
(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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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of q^(-1/12)*eta(q^2)^4*eta(q^6)^2/(eta(q)^2*eta(q^4)*eta(q^12)) in powers of q.
Euler transform of period 12 sequence [ 2, -2, 2, -1, 2, -4, 2, -1, 2, -2, 2, -2, ...].
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^4*eta(x^6+A)^2/ eta(x+A)^2/ eta(x^4+A)/ eta(x^12+A), n))}
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CROSSREFS
| Cf. A093829(12n+1)=a(n).
Sequence in context: A115116 A141662 A088062 * A178412 A182598 A067694
Adjacent sequences: A123881 A123882 A123883 * A123885 A123886 A123887
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Oct 17 2006
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