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A128145
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Expansion of psi(q^3)* phi(-q^3)* chi^2(-q^3)/( psi(-q)* phi(-q^18)) in powers of q where phi(),psi(),chi() are Ramanujan theta functions.
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2
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1, 1, 1, -1, 0, 1, 0, -1, -1, 2, 0, -3, 0, 2, 0, -3, 0, 5, 0, -4, 2, 4, 0, -5, 0, 7, -2, -7, 0, 5, 0, -10, -1, 12, 0, -10, 0, 14, 4, -17, 0, 21, 0, -22, -4, 24, 0, -34, 0, 33, -1, -36, 0, 45, 0, -45, 8, 52, 0, -55, 0, 62, -8, -71, 0, 70, 0, -88, -2, 96, 0, -98, 0, 122, 14, -133, 0, 148, 0, -163, -14, 182, 0, -217, 0, 216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,10
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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^3)^3* eta(q^36))/(eta(q)* eta(q^4)* eta(q^6)* eta(q^18)^2) in powers of q.
Euler transform of period 36 sequence [ 1, 0, -2, 1, 1, -2, 1, 1, -2, 0, 1, -1, 1, 0, -2, 1, 1, 0, 1, 1, -2, 0, 1, -1, 1, 0, -2, 1, 1, -2, 1, 1, -2, 0, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= (v-1)*(3-3*v+v^2)*(2*u-u^2)^2 -(u+v-u*v)^2*(u-v)^2.
a(6n+4)=0. a(6n)=0 if n>0.
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^36+A)*eta(x^3+A)^3/ (eta(x+A)*eta(x^4+A)*eta(x^6+A)*eta(x^18+A)^2), n))}
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CROSSREFS
| A092848(n)=a(6n+2). A128143(n)=a(n) if n>0. A128144(n)=-a(n) if n>0.
Sequence in context: A163496 A092241 A128144 * A128143 A027640 A194666
Adjacent sequences: A128142 A128143 A128144 * A128146 A128147 A128148
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Feb 16 2007
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