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Search: id:A131985
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| A131985 |
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Expansion of (eta(q^3)^2/( eta(q)* eta(q^9)))^6 in powers of q. |
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+0
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| 1, 6, 27, 86, 243, 594, 1370, 2916, 5967, 11586, 21870, 39852, 71052, 123444, 210654, 352480, 581013, 942786, 1510254, 2388204, 3734964, 5777788, 8852004, 13434984, 20218395, 30177684, 44704413, 65743348, 96033357, 139368816
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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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 +12*v^2 +u*w -v^2*(u+w) +12*v*(u+w) +27*v.
G.f. is Fourier series of a weight 0 level 9 modular form. f(-1/ (9 t)) = f(t) where q = exp(2 pi i t).
G.f.: (1/x)*(Product_{k>0} (1-x^(3k))^2/( (1-x^k)* (1-x^(9k))))^6.
Euler transform of period 9 sequence [ 6, 6, -6, 6, 6, -6, 6, 6, 0, ...].
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EXAMPLE
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1/q + 6 + 27*q + 86*q^2 + 243*q^3 + 594*q^4 + 1370*q^5 + 2916*q^6 +...
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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^3+A)^2/ eta(x+A)/ eta(x^9+A))^6, n))}
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CROSSREFS
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A007266(n)= a(n) unless n=0.
Sequence in context: A027313 A124089 A100188 this_sequence A125196 A100189 A052267
Adjacent sequences: A131982 A131983 A131984 this_sequence A131986 A131987 A131988
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 04 2007
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