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Search: id:A123864
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| A123864 |
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Expansion of (eta(q^3)eta(q^5))^2/(eta(q)eta(q^15)) in powers of q. |
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| 1, 1, 2, 1, 3, 1, 2, 0, 4, 1, 2, 0, 3, 0, 0, 1, 5, 2, 2, 2, 3, 0, 0, 2, 4, 1, 0, 1, 0, 0, 2, 2, 6, 0, 4, 0, 3, 0, 4, 0, 4, 0, 0, 0, 0, 1, 4, 2, 5, 1, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 3, 2, 4, 0, 7, 0, 0, 0, 6, 2, 0, 0, 4, 0, 0, 1, 6, 0, 0, 2, 5, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 6, 2, 4, 2, 6, 0, 2, 0, 3, 0, 4, 0, 0
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Euler transform of period 15 sequence [ 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -2, ...].
Moebius transform is period 15 sequence [ 1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=-v^3+4uvw-2uw^2-u^2w.
G.f.: Product_{k>0} ((1-x^(3k))*(1-x^(5k)))^2/((1-x^k)*(1-x^(15k))).
G.f.: (1/2)(Sum_{n,m} x^(n^2+n*m+4*m^2) +x^(2*n^2+n*m+2*m^2)).
a(15n+7)=a(15n+11)=a(15n+13)=a(15n+14)=0.
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, sumdiv(n, d, kronecker(-15, d)))}
(PARI) {a(n)=if(n<1, n==0, (qfrep([2, 1; 1, 8], n, 1)+qfrep([4, 1; 1, 4], n, 1))[n])}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^3+A)*eta(x^5+A))^2/(eta(x+A)*eta(x^15+A)), n))}
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CROSSREFS
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A035175(n)=a(n) if n>0.
Sequence in context: A106740 A110619 A129761 this_sequence A035175 A106406 A092412
Adjacent sequences: A123861 A123862 A123863 this_sequence A123865 A123866 A123867
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 14 2006
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