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Search: id:A131986
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| A131986 |
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Expansion of (eta(q)/ eta(q^9))^3 in powers of q. |
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+0
1
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| 1, -3, 0, 5, 0, 0, -7, 0, 0, 3, 0, 0, 15, 0, 0, -32, 0, 0, 9, 0, 0, 58, 0, 0, -96, 0, 0, 22, 0, 0, 149, 0, 0, -253, 0, 0, 68, 0, 0, 372, 0, 0, -599, 0, 0, 140, 0, 0, 826, 0, 0, -1317, 0, 0, 317, 0, 0, 1768, 0, 0, -2735, 0, 0, 632, 0, 0, 3526, 0, 0, -5434, 0, 0, 1259, 0, 0, 6854, 0, 0, -10364, 0
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Euler transform of period 9 sequence [ -3, -3, -3, -3, -3, -3, -3, -3, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u+v)^3 -u*v*(27 +9*(u+v) +u*v).
G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= u^2 +w^2 +u*w -v^2*(u+w) -6*v^2 -6*v*(u+w) -27*v.
G.f. is a Fourier series which satisfies f(-1/(9 t)) = 27/ f(t) where q = exp(2 pi i t).
a(3n+1)= 0. a(3n)= 0 unless n=0.
G.f.: (1/x)*(Product_{k>0} (1-x^k)/ (1-x^(9k)))^3.
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EXAMPLE
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1/q - 3 + 5*q^2 - 7*q^5 + 3*q^8 + 15*q^11 - 32*q^14 + 9*q^17 + ...
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PROGRAM
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(PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); polcoeff( (eta(x+A)/ eta(x^9+A))^3, n))}
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CROSSREFS
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A058091(n)= a(3n-1).
Adjacent sequences: A131983 A131984 A131985 this_sequence A131987 A131988 A131989
Sequence in context: A010816 A133089 A136599 this_sequence A002656 A122274 A003966
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 04 2007
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