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Search: id:A128143
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| A128143 |
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Expansion of q* (psi(q^9)/phi(q^9))/ (psi(q)/phi(q)) in powers of q where psi(),phi() are Ramanujan theta functions. |
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+0
3
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| 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, -4
(list; graph; listen)
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OFFSET
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1,9
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FORMULA
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Euler transform of period 36 sequence [ 1, -2, 1, 0, 1, -2, 1, 0, 0, -2, 1, 0, 1, -2, 1, 0, 1, 0, 1, 0, 1, -2, 1, 0, 1, -2, 0, 0, 1, -2, 1, 0, 1, -2, 1, 0, ...].
Expansion of eta(q^2)^3* eta(q^9)* eta(q^36)^2/ (eta(q)* eta(q^4)^2* eta(q^18)^3) in powers of q.
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=v* (1-v+v^2)* (1-u^2)^2 -(1-u*v)^2* (u-v)^2.
a(6n)=a(6n+4)=0.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^2+A)^3*eta(x^9+A)*eta(x^36+A)^2/ (eta(x+A)*eta(x^4+A)^2*eta(x^18+A)^3), n))}
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CROSSREFS
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A092848(n)=a(6n+2). A128144(n)=-a(n) if n>0. A128145(n)=a(n) if n>0.
Sequence in context: A092241 A128144 A128145 this_sequence A027640 A127460 A154109
Adjacent sequences: A128140 A128141 A128142 this_sequence A128144 A128145 A128146
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 16 2007
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