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A132217
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Expansion of psi(q^6)/ psi(-q) in powers of q where psi() is a Ramanujan theta functions.
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0
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1, 1, 1, 2, 3, 4, 6, 8, 11, 15, 19, 25, 33, 42, 53, 68, 86, 107, 134, 166, 205, 253, 309, 377, 460, 557, 672, 811, 974, 1166, 1394, 1661, 1975, 2344, 2773, 3275, 3863, 4543, 5333, 6253, 7316, 8544, 9964, 11600, 13484, 15653, 18140, 20994, 24269, 28011, 32288
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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^(-5/8)* eta(q^2)* eta(q^12)^2/( eta(q)* eta(q^4)* eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, ...].
Product_{k>0} (1-x^(12*k))* (1-x^(2*k)+x^(4*k))/ (1-x^k).
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PROG
| (PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^2+A)* eta(x^12+A)^2/ eta(x+A)/ eta(x^4+A)/ eta(x^6+A), n))}
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CROSSREFS
| Sequence in context: A117995 A033834 A127419 * A039855 A175868 A035950
Adjacent sequences: A132214 A132215 A132216 * A132218 A132219 A132220
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 13 2007
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