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A131796
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Expansion of chi(-q^3)^2*chi(-q^5)^2/(chi(-q)*chi(-q^15)) in powers of q where chi() is a Ramanujan theta function.
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2
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1, 1, 1, 0, 0, -1, -1, 0, 1, 0, -1, 0, 0, 1, 2, 1, -2, -3, -1, 1, 2, 3, 0, -3, -1, 2, 2, 0, -2, -6, -3, 4, 7, 3, -2, -5, -6, 2, 8, 3, -5, -6, -2, 4, 12, 7, -10, -15, -6, 5, 13, 12, -4, -18, -7, 11, 14, 6, -10, -24, -14, 20, 32, 12, -12, -29, -24, 9, 36, 15, -22, -30, -13, 22, 50, 27, -36, -63, -26, 24, 56, 45, -22, -69, -30, 42, 62
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,15
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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
| Euler transform of period 30 sequence [ 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= v^2 +u*(2 -4*v +u*v).
G.f.: Product_{k>0} (1+x^k)* (1+x^(15*k))/ ((1+x^(3*k))* (1+x^(5*k)))^2.
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PROG
| (PARI) {a(n)=if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^30+A)/eta(x+A)/eta(x^15+A)* (eta(x^3+A)*eta(x^5+A)/eta(x^6+A)/eta(x^10+A))^2, n))}
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CROSSREFS
| Cf. A131794(n)= a(n) unless n=0. A131797(n)= -a(n) unless n=0.
Sequence in context: * A131797 A145727 A145782 A131794 A145726 A181631
Adjacent sequences: A131793 A131794 A131795 * A131797 A131798 A131799
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Jul 16 2006
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