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A121362
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Expansion of eta(q)*eta(q^6)*eta(q^10)*eta(q^15)/(eta(q^3)*eta(q^5)) in powers of q.
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3
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1, -1, -1, 1, -1, 1, 0, -1, 1, 1, 0, -1, 0, 0, 1, 1, -2, -1, 2, -1, 0, 0, -2, 1, 1, 0, -1, 0, 0, -1, 2, -1, 0, 2, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, -1, 2, -2, -1, 1, -1, 2, 0, -2, 1, 0, 0, -2, 0, 0, 1, 2, -2, 0, 1, 0, 0, 0, -2, 2, 0, 0, -1, 0, 0, -1, 2, 0, 0, 2, -1, 1, 0, -2, 0, 2, 0, 0, 0, 0, 1, 0, -2, -2, 2, -2, 1, 0, -1, 0, 1, 0, -2, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,17
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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, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -2, ...].
Expansion of q*f(-q)f(-q^15)/(chi(-q^3)chi(-q^5)) in powers of q where f(),chi() are Ramanujan theta functions.
G.f.: x Product_{n>0} (1-x^n)(1+x^(3n))(1+x^(5n))(1-x^(15n)).
a(n) is multiplicative with a(2^e)=a(3^e)=a(5^e)=(-1)^e, a(p^e) = e+1 if p == 1,4 (mod 15), a(p^e) = (-1)^e*(e+1) if p == 2,8 (mod 15), a(p^e) = (1+( -1)^e)/2 if p == 7,11,13,14 (mod 15).
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PROG
| (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^6+A)*eta(x^10+A)*eta(x^15+A)/(eta(x^3+A)*eta(x^5+A)), n))}
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CROSSREFS
| Cf. A082451(n)=|a(n)|.
Sequence in context: A048622 A105661 A082451 * A091704 A175799 A123739
Adjacent sequences: A121359 A121360 A121361 * A121363 A121364 A121365
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Jul 22 2006
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