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Search: id:A118271
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| A118271 |
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Expansion of (9theta_4(q^3)^4-theta_4(q)^4)/8 in powers of q. |
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2
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| 1, 1, -3, -5, -3, 6, 15, 8, -3, -23, -18, 12, 15, 14, -24, -30, -3, 18, 69, 20, -18, -40, -36, 24, 15, 31, -42, -77, -24, 30, 90, 32, -3, -60, -54, 48, 69, 38, -60, -70, -18, 42, 120, 44, -36, -138, -72, 48, 15, 57, -93, -90, -42, 54, 231, 72, -24, -100, -90, 60, 90, 62, -96, -184, -3, 84, 180, 68, -54, -120, -144
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Expansion of eta(q^2)^5*et(q^3)^3/(eta(q)eta(q^6)^3) in powers of q.
Euler transform of period 6 sequence [ 1, -4, -2, -4, 1, -4, ...].
a(n) is multiplicative with a(2^e) = -3 if e>0, a(3^e) = 4-3^(e+1), a(p^e) = (p^(e+1)-1)/(p-1) if p>3.
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( sum(k=1, sqrtint(n), 2*(-x)^k^2, 1+x*O(x^n))^4 -9*sum(k=1, sqrtint(n\3), 2*(-x^3)^k^2, 1+x*O(x^n))^4, n)/-8)}
(PARI) {a(n)= if(n<1, n==0, -(-1)^n*( sumdiv(n, d, d*(1-if(d%3==0, 3)-if(d%4==0, 1)+if(d%12==0, 3)))))}
(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, -3, if(p==3, 4-3^(e+1), (p^(e+1)-1)/(p-1))))))}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^5*eta(x^3+A)^3/ eta(x+A)/ eta(x^6+A)^3, n))}
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CROSSREFS
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A118272(n)=-a(3n+2)/3. A109506(3n)=a(3n). A109056(3n+1)=a(3n+1).
Sequence in context: A134429 A100667 A096438 this_sequence A095366 A029604 A079602
Adjacent sequences: A118268 A118269 A118270 this_sequence A118272 A118273 A118274
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Apr 21 2006
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