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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
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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; refs; listen; history; internal format)
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OFFSET
| -1,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| 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
| 1/q + 4 + 10*q + 24*q^2 + 51*q^3 + 100*q^4 + 190*q^5 + 340*q^6 + ...
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PROG
| (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
| A058504(n)=a(n) if n nonzero.
Sequence in context: A143696 A058514 A001979 * A022569 A093831 A052365
Adjacent sequences: A128513 A128514 A128515 * A128517 A128518 A128519
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 06 2007
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