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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,17
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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REFERENCES
| B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 377, Entry 9(i).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| 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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PROG
| (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
| Sequence in context: A134023 A015738 A115604 * A116488 A145765 A157424
Adjacent sequences: A128614 A128615 A128616 * A128618 A128619 A128620
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 13 2007
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