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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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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,9
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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 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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PROG
| (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
| 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 * A027640 A194666 A127460
Adjacent sequences: A128140 A128141 A128142 * A128144 A128145 A128146
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Feb 16 2007
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