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Search: id:A128519
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| A128519 |
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Expansion of q^(-1)* chi(-q)* chi(-q^39)/ (chi(-q^3)* chi(-q^13)) in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 2, -2, 1, 0, 1, -3, 4, -3, 2, -1, 2, -4, 5, -5, 3, -2, 3, -6, 8, -7, 4, -2, 5, -9, 11, -10, 6, -4, 6, -12, 16, -14, 8, -6, 11, -17, 21, -19, 13, -10, 14, -24, 30, -26, 17, -14, 21, -31, 38, -35, 25, -20, 26, -42, 52, -46, 33, -28, 38, -56, 68, -62, 47, -38, 49, -75
(list; graph; listen)
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OFFSET
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-1,13
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FORMULA
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G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= (u^2-v)* (w^2-v) +u*w* (2*(1+v^2) +4*v).
Euler transform of a period 78 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1/(78t))= 1/f(t) where q= exp(2 pi i t).
G.f.: (1/x)* (Product_{k>0} P(x^k))^-1 where P(x) is the 78th cyclotomic polynomial of degree 24.
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EXAMPLE
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1/q - 1 - q^4 + q^5 - q^6 + q^7 - q^10 + 2*q^11 - q^12 + q^15 + ...
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PROGRAM
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(PARI) {a(n)= if(n<-1, 0, n++; A=x*O(x^n); polcoeff( eta(x+A)* eta(x^6+A) *eta(x^26+A)* eta(x^39+A)/ (eta(x^2+A)* eta(x^3+A)* eta(x^13+A)* eta(x^78+A)), n))}
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CROSSREFS
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A058755(n)=a(n) if n nonzero.
Sequence in context: A048571 A025880 A058755 this_sequence A061670 A108063 A164846
Adjacent sequences: A128516 A128517 A128518 this_sequence A128520 A128521 A128522
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 06 2007
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