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Search: id:A128616
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| A128616 |
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Expansion of q* psi(q^3)* psi(q^5) in powers of q where psi() is a Ramanujan theta function. |
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+0
1
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| 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,19
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 377, Entry 9(iv).
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FORMULA
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Expansion of (eta(q^6)* eta(q^10))^2/ (eta(q^3)* eta(q^5)) in powers of q.
Euler transform of period 30 sequence [ 0, 0, 1, 0, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0, 2, 0, 0, -1, 0, -1, 1, 0, 0, -1, 1, 0, 1, 0, 0, -2, ...].
For n>0, n in A028957 equivalent to a(n) nonzero. If a(n) nonzero, a(n)= A082451(n) and a(n)= A121362(n).
a(n)= (A082451(n)+ A121362(n))/2.
G.f.: x* Product_{k>0} (1-x^(3k))* (1-x^(5k))* (1+x^(6k))^2* (1+x^(10k))^2.
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PROGRAM
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(PARI) {a(n)= if(n<1, 0, sumdiv(n, d, kronecker(-60, d) +kronecker(20, d)* kronecker(-3, n/d) )/2)}
(PARI) {a(n)= local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x^6+A)* eta(x^10+A))^2/ (eta(x^3+A)* eta(x^5+A)), n))}
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CROSSREFS
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Sequence in context: A101668 A141846 A035202 this_sequence A101257 A144629 A025907
Adjacent sequences: A128613 A128614 A128615 this_sequence A128617 A128618 A128619
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 13 2007
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