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Search: id:A128617
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| A128617 |
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Expansion of q^2* psi(q)* psi(q^15) in powers of q where psi() is a Ramanujan theta function. |
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2
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| 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,17
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 377, Entry 9(i).
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FORMULA
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Expansion of (eta(q^2)* eta(q^30))^2/ (eta(q)* eta(q^15)) in powers of q.
Euler transform of period 30 sequence [ 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 2, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -2, ...].
For n>0, n in A028955 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^2* Product_{k>0} (1-x^k)* (1-x^(15k))* (1+x^(2k))^2* (1+x^(30k))^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<2, 0, n-=2; A=x*O(x^n); polcoeff( (eta(x^2+A)* eta(x^30+A))^2/ (eta(x+A)* eta(x^15+A)), n))}
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CROSSREFS
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Adjacent sequences: A128614 A128615 A128616 this_sequence A128618 A128619 A128620
Sequence in context: A134023 A015738 A115604 this_sequence A116488 A135929 A080733
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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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