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A128762
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Expansion of chi(q)* chi(q^2)/ (chi(q^5)* chi(q^10)) in powers of q where chi() is a Ramanujan theta function.
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1
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1, 1, 1, 2, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5, 6, 6, 8, 9, 10, 12, 14, 15, 17, 20, 21, 23, 26, 30, 32, 37, 42, 44, 50, 56, 60, 66, 74, 80, 88, 98, 109, 119, 130, 144, 154, 167, 184, 200, 218, 241, 262, 284, 308, 334, 362, 390, 426, 462, 498, 542, 589, 633, 685, 742, 796, 858
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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 40 sequence [ 1, 0, 1, -1, 0, 0, 1, 0, 1, 0, 1, -1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, -1, 1, 0, 1, 0, 1, 0, 0, -1, 1, 0, 1, 0, ...].
Given g.f. A(x), then B(x)= x*A(x^2) satisfies 0= f(B(x), B(x^3)) where f(u, v)= (u-v^3)* (u^3-v) -3*u*v* (u^2+v^2).
G.f.: Product_{k>0} (1+x^k)* (1+x^(20k))/( (1+x^(4k))* (1+x^(5k))).
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EXAMPLE
| q + q^3 + q^5 + 2*q^7 + q^9 + q^11 + 2*q^13 + 2*q^15 + 2*q^17 + ...
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PROG
| (PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x+A)* eta(x^8+A)* eta(x^10+A)* eta(x^20+A)/ (eta(x^2+A)* eta(x^4+A)* eta(x^5+A)* eta(x^40+A)), n))}
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CROSSREFS
| Convolution inverse of A128763.
Sequence in context: A029255 A029272 A153904 * A126307 A092332 A092334
Adjacent sequences: A128759 A128760 A128761 * A128763 A128764 A128765
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 25 2007
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