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Search: id:A122777
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| A122777 |
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Expansion of eta(q^3)eta(q^5)eta(q^6)eta(q^10)-eta(q)eta(q^2)eta(q^15)eta(q^30) in powers of q. |
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+0
2
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| 1, -1, 1, 1, -1, -1, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1, -4, 0, 0, -1, 1, -2, 1, -4, -6, 1, 8, -1, 0, -6, 4, 1, 2, 4, 2, 1, -6, 4, -4, 0, -1, 0, 0, 1, 9, -1, 6, 2, -6, -1, 0, 4, -4, 6, 0, -1, -10, -8, -4, 1, -2, 0, -4, 6, 0, -4, 0, -1, 2, -2, 1, -4, 0, -2, 8, -1, 1, 6, 12, -4, -6, 4, -6, 0, 18, 1, -8, 0, 8, 0, 4, -1, 2, -9, 0, 1, 18, -6, -4
(list; graph; listen)
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OFFSET
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1,7
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FORMULA
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G.f.: x Product_{k>0} (1-x^(3k))(1-x^(5k))(1-x^(6k))(1-x^(10k)) - x^2 Product_{k>0} (1-x^k)(1-x^(2k))(1-x^(15k))(1-x^(30k)).
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^3+A)*eta(x^5+A)*eta(x^6+A)*eta(x^10+A)- eta(x+A)*eta(x^2+A)*eta(x^15+A)*eta(x^30+A)*x, n))}
(PARI) {a(n)=local(A); if(n<1, 0, n*=2; n--; A=x*O(x^n); A=eta(x^2+A)*eta(x^3+A)^3/eta(x+A)/eta(x^6+A); A=A*subst(A+x*O(x^(n\5)), x, x^5); polcoeff(A, n))}
(PARI) {a(n)= local(A, p, e, x, y, a0, a1); if(n<1, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2|p==5, (-1)^e, if(p==3, 1, a1=y=-sum(x=0, p-1, kronecker(6*x^3+x^2+4*x+4, p)); a0=1; for(i=2, e, x=y*a1-p*a0; a0=a1; a1=x); a1)))))}
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CROSSREFS
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A122779(2n)=a(n).
Sequence in context: A128760 A057884 A016684 this_sequence A103524 A110916 A164561
Adjacent sequences: A122774 A122775 A122776 this_sequence A122778 A122779 A122780
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Sep 10 2006
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