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Search: id:A128516
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| A128516 |
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Expansion of q^(-1)* (chi(-q^7)/ chi(-q))^4 in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, 4, 10, 24, 51, 100, 190, 340, 585, 984, 1606, 2564, 4022, 6188, 9382, 14044, 20746, 30308, 43836, 62784, 89153, 125588, 175542, 243656, 335988, 460388, 627178, 849676, 1145024, 1535416, 2049200, 2722544, 3601681, 4745208, 6227276, 8141656
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Expansion of (eta(q^2)* eta(q^7)/ (eta(q)* eta(q^14)))^4 in powers of q.
Euler transform of period 14 sequence [ 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, 0, 4, 0, ...].
G.f. is Fourier series of a level 14 modular function. f(-1/(14t))= f(t) where q= exp(2 pi i t).
G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= (u^2-v)* (w^2-v) -u*w* (8*(1+v^2) -16*v).
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u*v +1)* (u+v)* (u-v)^2 -u*v* (u-1)* (v-1)* (u*v -8*(u+v) +1).
G.f.: (1/x)* (Product_{k>0} P(x^k))^-4 where P(x)= x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 is the 14th cyclotomic polynomial.
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EXAMPLE
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1/q + 4 + 10*q + 24*q^2 + 51*q^3 + 100*q^4 + 190*q^5 + 340*q^6 + ...
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PROGRAM
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(PARI) {a(n)= if(n<-1, 0, n++; A=x*O(x^n); polcoeff( (eta(x^2+A)* eta(x^7+A)/ (eta(x+A)* eta(x^14+A)))^4, n))}
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CROSSREFS
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A058504(n)=a(n) if n nonzero.
Sequence in context: A143696 A058514 A001979 this_sequence A022569 A093831 A052365
Adjacent sequences: A128513 A128514 A128515 this_sequence A128517 A128518 A128519
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 06 2007
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