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Search: id:A132091
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| A132091 |
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Expansion of psi(q^3)* chi(-q^9)/ f(-q^2) in powers of q where psi(), chi(), f() are Ramanujan theta functions. |
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1
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| 1, 0, 1, 1, 2, 1, 3, 2, 5, 3, 7, 5, 10, 7, 14, 11, 20, 15, 27, 22, 37, 30, 49, 42, 66, 56, 86, 75, 113, 99, 146, 131, 189, 170, 241, 221, 308, 283, 389, 363, 492, 460, 616, 583, 771, 732, 958, 918, 1189, 1143, 1467, 1421, 1807, 1756, 2215, 2166, 2711, 2658, 3303, 3256
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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Expansion of q^(1/12)* eta(q^6)^2* eta(q^9)/( eta(q^2)* eta(q^3)* eta(q^18)) in powers of q.
Euler transform of period 18 sequence [ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, ...].
G.f.: Product_{k>0} (1+x^(2*k)+x^(4*k))/ (1-x^(3*k)+x^(6*k)).
G.f.: Sum_{k>=0} Product_{0<i<=k} x^(4*i-2)* (1-x^(6*i-3))/( (1-x^(2*i-1))* (1-x^(4*i-2))* (1-x^(4*i))).
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PROGRAM
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(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^6+A)^2* eta(x^9+A)/ eta(x^2+A)/ eta(x^3+A)/ eta(x^18+A), n))}
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CROSSREFS
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Sequence in context: A029138 A008731 A114209 this_sequence A051792 A053602 A123231
Adjacent sequences: A132088 A132089 A132090 this_sequence A132092 A132093 A132094
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 09 2007
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