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Search: id:A128763
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| A128763 |
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Expansion of chi(q^5)* chi(q^10)/( chi(q)* chi(q^2)) in powers of q where chi() is a Ramanujan theta function. |
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+0
2
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| 1, -1, 0, -1, 2, -1, 0, -2, 3, -2, 2, -4, 6, -5, 4, -6, 9, -8, 6, -10, 15, -14, 12, -17, 24, -21, 18, -26, 35, -32, 30, -42, 52, -50, 48, -60, 75, -74, 70, -88, 111, -109, 104, -130, 158, -154, 150, -184, 220, -218, 218, -262, 308, -308, 308, -362, 421, -426, 428, -498, 580, -589, 592, -685, 788, -796
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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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)= 1/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^(4k))* (1+x^(5k))/( (1+x^k)* (1+x^(20k)) ).
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EXAMPLE
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1/q - q - q^5 + 2*q^7 - q^9 - 2*q^13 + 3*q^15 - 2*q^17 + 2*q^19 - ...
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PROGRAM
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(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
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Convolution inverse of A128762.
Sequence in context: A111374 A072739 A030399 this_sequence A127597 A167749 A104770
Adjacent sequences: A128760 A128761 A128762 this_sequence A128764 A128765 A128766
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 25 2007
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