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Search: id:A128764
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| A128764 |
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Expansion of chi(q)/ chi(q^13) in powers of q where chi() is a Ranaujan theta function. |
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+0
1
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| 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 4, 4, 4, 4, 5, 6, 6, 6, 7, 9, 9, 10, 12, 12, 13, 14, 16, 18, 19, 20, 23, 26, 26, 28, 30, 33, 37, 38, 42, 46, 49, 52, 56, 62, 65, 70, 76, 84, 89, 92, 101, 110, 117, 123, 133, 145, 153, 162, 174, 188, 197, 208, 227, 242, 256, 270, 290
(list; graph; listen)
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OFFSET
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0,9
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FORMULA
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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 -u*v).
Euler transform of period 52 sequence [ 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, ...].
G.f.: Product_{k>0} (1+x^k)* (1+x^(26k))/( (1+x^(2k))* (1+x^(13k)) ).
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EXAMPLE
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q + q^3 + q^7 + q^9 + q^11 + q^13 + 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^2+A)^2* eta(x^13+A)* eta(x^52+A)/ (eta(x+A)* eta(x^4+A)* eta(x^26+A)^2), n))}
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CROSSREFS
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Sequence in context: A067595 A134868 A127417 this_sequence A074589 A165035 A081309
Adjacent sequences: A128761 A128762 A128763 this_sequence A128765 A128766 A128767
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 25 2007
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