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Search: id:A082564
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| A082564 |
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Expansion of eta(q)^2* eta(q^2)/ eta(q^4) in powers of q. |
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2
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| 1, -2, -2, 4, 2, 0, -4, 0, 2, -6, 0, 4, 4, 0, 0, 0, 2, -4, -6, 4, 0, 0, -4, 0, 4, -2, 0, 8, 0, 0, 0, 0, 2, -8, -4, 0, 6, 0, -4, 0, 0, -4, 0, 4, 4, 0, 0, 0, 4, -2, -2, 8, 0, 0, -8, 0, 0, -8, 0, 4, 0, 0, 0, 0, 2, 0, -8, 4, 4, 0, 0, 0, 6, -4, 0, 4, 4, 0, 0, 0, 0, -10, -4, 4, 0, 0, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, -4, -2, 12, 2, 0, -8, 0
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Absolute values appear to give A033715=2*A002325.
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FORMULA
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Expansion of phi(-q)*phi(-q^2) in powers of q where phi() is a Ramanujan theta function.
Euler transform of period 4 sequence [ -2, -3, -2, -2, ...]. - Michael Somos Mar 30 2007
G.f.: Product_{k>0} (1-x^k)^2/ (1+x^(2k)) .
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PROGRAM
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(PARI) {a(n)= if(n<1, n==0, 2*(-1)^((n+1)\2)* sumdiv(n, d, kronecker(-8, d)))} /* Michael Somos Mar 30 2007 */
(PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)^2* eta(x^2+A)/ eta(x^4+A), n))}
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CROSSREFS
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-2*A129134(n)= a(n) if n>0.
Sequence in context: A129355 A080963 A033715 this_sequence A133692 A139093 A080918
Adjacent sequences: A082561 A082562 A082563 this_sequence A082565 A082566 A082567
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KEYWORD
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sign
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2003
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