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Search: id:A131794
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| A131794 |
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Expansion of q* psi(q)* psi(q^15)/ (psi(q^3)* psi(q^5)) in powers of q where psi() is a Ramanujan theta function. |
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+0
4
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| 1, 1, 0, 0, -1, -1, 0, 1, 0, -1, 0, 0, 1, 2, 1, -2, -3, -1, 1, 2, 3, 0, -3, -1, 2, 2, 0, -2, -6, -3, 4, 7, 3, -2, -5, -6, 2, 8, 3, -5, -6, -2, 4, 12, 7, -10, -15, -6, 5, 13, 12, -4, -18, -7, 11, 14, 6, -10, -24, -14, 20, 32, 12, -12, -29, -24, 9, 36, 15, -22, -30, -13, 22, 50, 27, -36, -63, -26, 24, 56, 45, -22, -69, -30, 42, 62, 27
(list; graph; listen)
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OFFSET
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1,14
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FORMULA
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Euler transform of period 30 sequence [ 1, -1, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0, 1, -1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, 1, 0, ...].
Expansion of eta(q^2)^2* eta(q^3)* eta(q^5)* eta(q^30^2)/(eta(q)* eta(q^6)^2* eta(q^10)^2* eta(q^15)) in powers of q.
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u^2-v)* (1+v) -2*v* (u-v).
G.f.: x* Product_{k>0} P_15(x^k)* P_30(x^k)^2 where P_n() is the n-th cyclotomic polynomial.
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PROGRAM
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(PARI) {a(n)= local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^3+A)* eta(x^5+A)/ eta(x+A)/ eta(x^15+A)* (eta(x^2+A)* eta(x^30+A)/ eta(x^6+A)/ eta(x^10+A))^2, n))}
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CROSSREFS
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A131796(n)= a(n) unless n=0. A131797(n)= -a(n) unless n=0.
Adjacent sequences: A131791 A131792 A131793 this_sequence A131795 A131796 A131797
Sequence in context: A138243 A131796 A131797 this_sequence A133674 A098666 A133232
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 16 2007
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