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Search: id:A137676
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| A137676 |
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Expansion of f(-q^2) * f(-q^5) / ( f(-q^4) * f(-q, -q^4) ) in powers of q where f(,) is Ramanujan's two-variable theta function. |
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1
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| 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 3, 3, 0, 0, 4, 4, 0, 0, 5, 6, 0, 0, 7, 7, 0, 0, 9, 10, 0, 0, 12, 12, 0, 0, 15, 16, 0, 0, 19, 20, 0, 0, 24, 26, 0, 0, 30, 31, 0, 0, 37, 40, 0, 0, 46, 48, 0, 0, 57, 60, 0, 0, 69, 72, 0, 0, 84, 89, 0, 0, 102, 106, 0, 0, 123, 130, 0, 0, 148, 154, 0, 0
(list; graph; listen)
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OFFSET
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0,10
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REFERENCES
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G. E. Andrews, q-series, CBMS Regional Conference Series in Mathematics, 66, Amer. Math. Soc. 1986, see p. 36, Eq. (4.11). MR0858826 (88b:11063)
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FORMULA
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Expansion of ( f(-q^13, -q^17) + q * f(-q^7, -q^23) ) / f(-q^4) in powers of q where f(,) is Ramanujan's two-variable theta function.
Euler transform of period 20 sequence [ 1, -1, 0, 1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 1, 0, -1, 1, 0, ...].
a(4*n+2) = a(4*n+3) = 0.
G.f.: sum_{k>=0} x^k^2 / ( Product_{j=1..k} 1 - x^(4*j) ).
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EXAMPLE
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1 + q + q^4 + q^5 + q^8 + 2*q^9 + 2*q^12 + 2*q^13 + 3*q^16 + 3*q^17 + ...
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, sqrtint(n), x^k^2 / prod(i=1, k, 1 - x^(4*i), 1+x*O(x^(n-k^2)))), n))}
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CROSSREFS
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A122129(n) = a(4*n). A122135(n) = a(4*n+1).
Sequence in context: A122071 A099766 A132339 this_sequence A144734 A029361 A107502
Adjacent sequences: A137673 A137674 A137675 this_sequence A137677 A137678 A137679
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Feb 04 2008
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