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A128770
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Expansion of phi(-q^9)/phi(-q) in powers of q where phi() is a Ramanujan theta function.
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2
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1, 2, 4, 8, 14, 24, 40, 64, 100, 152, 228, 336, 488, 700, 992, 1392, 1934, 2664, 3640, 4936, 6648, 8896, 11832, 15648, 20584, 26942, 35096, 45512, 58768, 75576, 96816, 123568, 157156, 199200, 251676, 316992, 398072, 498460, 622448, 775216, 963012
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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^9)^2/( eta(q)^2* eta(q^18) ) in powers of q.
Euler transform of period 18 sequence [ 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u-1)* (v^2-u) -2*u*v* (1-v).
G.f. A(x) satisfies 0= f(A(x), A(x^3)) where f(u, v)= (v-u)^3 -v*(3*u-1)* (1-v)* (1 -2*v +3*u*v).
G.f.: Product_{k>0} (1+x^k)* (1-x^(9k))/( (1-x^k)* (1+x^(9k)) ).
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PROG
| (PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^oo); polcoeff( eta(x^2+A)* eta(x^9+A)^2/ eta(x+A)^2/ eta(x^18+A), n))}
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CROSSREFS
| Convolution inverse of A128771. 2*A128129(n)= a(n) if n>0.
Sequence in context: A091779 A090399 A069251 * A069252 A069253 A004402
Adjacent sequences: A128767 A128768 A128769 * A128771 A128772 A128773
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 27 2007
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