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A128129
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Expansion of (chi(-q^3)/ chi^3(-q) -1)/3 in powers of q where chi() is a Ramanujan theta function.
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5
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1, 2, 4, 7, 12, 20, 32, 50, 76, 114, 168, 244, 350, 496, 696, 967, 1332, 1820, 2468, 3324, 4448, 5916, 7824, 10292, 13471, 17548, 22756, 29384, 37788, 48408, 61784, 78578, 99600, 125838, 158496, 199036, 249230, 311224, 387608, 481506, 596676
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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)^3* eta(q^3)/ (eta(q)^3* eta(q^6)) -1)/3 in powers of q.
Euler transform of period 18 sequence [ 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v -2*v^2 -4*u*v -6*u*v^2.
G.f. A(x) satisfies 0=f(A(x), A(x^3)) where f(u, v)= u^3 -v* (1+3*v+3*v^2)* (1+6*u+12*u^2).
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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)* eta(x^3+A)* eta(x^18+A)^2/ (eta(x^6+A)* eta(x^9+A)* eta(x+A)^2), n))}
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CROSSREFS
| A128128(n)=3*a(n) if n>0.
Sequence in context: A036372 A132218 A101230 * A014968 A126348 A006731
Adjacent sequences: A128126 A128127 A128128 * A128130 A128131 A128132
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Feb 15 2007
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