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Search: id:A129402
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| A129402 |
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Expansion of phi(q^3)* psi(q^4) +q* phi(q)* psi(q^12) in powers of q where phi(), psi() are Ramanujan theta functions. |
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1
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| 1, 1, 2, 2, 1, 2, 0, 2, 0, 0, 2, 0, 3, 1, 2, 2, 2, 4, 0, 0, 0, 0, 2, 0, 3, 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 2, 3, 4, 2, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 3, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 0, 4, 3, 2, 2, 0, 4, 0, 2, 0, 0, 4, 0, 1, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 83, Eq. (32.57).
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FORMULA
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Euler transform of period 24 sequence [ 1, 1, 0, -2, 1, -1, 1, -1, 0, 1, 1, -2, 1, 1, 0, -1, 1, -1, 1, -2, 0, 1, 1, -2, ...].
a(n)=b(2n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(3^e) = 1, b(p^e) = e+1 if p == 1, 5, 7, 11 (mod 24), b(p^e) = (1+(-1)^e)/2 if p == 13, 17, 19, 23 (mod 24).
a(12n+6)= a(12n+8)= a(12n+9)= a(12n+11)= 0. a(3n+1)= a(n).
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PROGRAM
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(PARI) {a(n)= if(n<0, 0, n=2*n+1; sumdiv(n, d, kronecker(-6, d)))}
(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^3+A)* eta(x^4+A)^3* eta(x^6+A)* eta(x^24+A)/ (eta(x+A)* eta(x^8+A)* eta(x^12+A)^2), n))}
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CROSSREFS
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A000377(2n+1)= a(n). A128582(n)= a(3n+2)/2. A113780(n)= a(12n).
Sequence in context: A043754 A094022 A128580 this_sequence A134177 A104405 A089077
Adjacent sequences: A129399 A129400 A129401 this_sequence A129403 A129404 A129405
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Apr 13 2007
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