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Search: id:A124452
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| A124452 |
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Expansion of psi(-q)psi(-q^2)chi(q^3)chi(q^6) in powers of q where psi(),chi() are Ramanujan theta functions. |
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1
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| 1, -1, -1, 1, -1, 0, 1, 0, -1, 3, 0, -2, 1, 0, 0, 0, -1, -2, 3, -2, 0, 0, -2, 0, 1, -1, 0, 5, 0, 0, 0, 0, -1, 2, -2, 0, 3, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, 0, 1, -1, -1, 2, 0, 0, 5, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, 2, -2, -2, 0, 0, 0, 3, -2, 0, 1, -2, 0, 0, 0, 0, 7, -2, -2, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 1, -2, -1, 6, -1, 0, 2, 0, 0
(list; graph; listen)
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OFFSET
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0,10
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FORMULA
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a(n)=-b(n) where b(n) is multiplicative with b(2^e) = 1, b(3^e) = 1-2*e, b(p^e) = 1+e if p == 1, 3 (mod 8), b(p^e) = (1+(-1)^e)/2 if p == 5, 7 (mod 8).
Euler transform of period 24 sequence [ -1, -1, 0, -1, -1, -1, -1, -2, 0, -1, -1, -2, -1, -1, 0, -2, -1, -1, -1, -1, 0, -1, -1, -2, ...].
Moebius transform is period 24 sequence [ -1, 0, 2, 0, 1, 0, 1, 0, 2, 0, -1, 0, 1, 0, -2, 0, -1, 0, -1, 0, -2, 0, 1, 0, ...].
a(8n+5)=a(8n+7)=0. a(2n)=a(n). a(3n)>=0.
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PROGRAM
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(PARI) {a(n)=local(A, p, e); if(n<1, n==0, A=factor(n); -prod( k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, 1, if(p==3, 1-2*e, if(p%8<4, e+1, !(e%2)))))))}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^6+A)* eta(x^8+A)*eta(x^12+A)/ (eta(x^3+A)*eta(x^24+A)), n))}
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CROSSREFS
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Sequence in context: A171759 A073538 A072780 this_sequence A004603 A092926 A052311
Adjacent sequences: A124449 A124450 A124451 this_sequence A124453 A124454 A124455
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Nov 02 2006
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