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Search: id:A128771
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| A128771 |
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Expansion of phi(-q)/phi(-q^9) in powers of q where phi() is a Ramanujan theta function. |
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3
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| 1, -2, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 2, 0, 0, -8, 0, 0, 8, 0, 0, 2, 0, 0, -16, 0, 0, 16, 0, 0, 4, 0, 0, -28, 0, 0, 28, 0, 0, 8, 0, 0, -48, 0, 0, 46, 0, 0, 12, 0, 0, -80, 0, 0, 76, 0, 0, 20, 0, 0, -126, 0, 0, 120, 0, 0, 32, 0, 0, -196, 0, 0, 184, 0, 0, 48, 0, 0, -300, 0, 0, 280, 0, 0, 72, 0, 0
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of eta(q)^2* eta(q^18)/( eta(q^2)* eta(q^9)^2 ) in powers of q.
Euler transform of period 18 sequence [ -2, -1, -2, -1, -2, -1, -2, -1, 0, -1, -2, -1, -2, -1, -2, -1, -2, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (1-u)* (u-v^2) -2*u* (v-1).
G.f. A(x) satisfies 0= f(A(x), A(x^3)) where f(u, v)= (u-v)^3 -u* (3-u)* (v-1)* (3 -2*u +u*v).
G.f.: Product_{k>0} (1-x^k)* (1+x^(9k))/( (1+x^k)* (1-x^(9k)) ).
a(3n+2)= a(3n+3)= 0.
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PROGRAM
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(PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^oo); polcoeff( eta(x+A)^2* eta(x^18+A)/ eta(x^2+A)/ eta(x^9+A)^2, n))}
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CROSSREFS
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Convolution inverse of A128770. -2*A092848(n)= a(3n+1).
Sequence in context: A127826 A109983 A093492 this_sequence A139380 A000122 A002448
Adjacent sequences: A128768 A128769 A128770 this_sequence A128772 A128773 A128774
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 27 2007
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