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Search: id:A121597
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| A121597 |
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Expansion of (eta(q^13)/eta(q))^2 in powers of q. |
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+0
2
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| 1, 2, 5, 10, 20, 36, 65, 110, 185, 300, 481, 752, 1165, 1768, 2661, 3946, 5802, 8430, 12158, 17360, 24622, 34632, 48410, 67188, 92731, 127182, 173546, 235508, 318098, 427536, 572168, 762318, 1011660, 1337136, 1760876, 2310338, 3021008, 3936848
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Euler transform of period 13 sequence [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=u^3+v^3-u*v-4*u*v*(u+v)-13*u^2*v^2.
G.f.: x*(Product_{k>0} (1-x^(13k))/(1-x^k))^2.
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u^2 - u*v + v^2)^2 - u*v * (1 + 6*u + 13*u^2) * (1 + 6*v + 13*v^2).
G.f. is a period 1 Fourier series which satisfies f(-1 / (13 t)) = (1/13) / f(t) where q = exp(2 pi i t).
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EXAMPLE
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q + 2*q^2 + 5*q^3 + 10*q^4 + 20*q^5 + 36*q^6 + 65*q^7 + 110*q^8 + ...
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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^13+A)/eta(x+A))^2, n))}
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CROSSREFS
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Convolution inverse of A133099.
Adjacent sequences: A121594 A121595 A121596 this_sequence A121598 A121599 A121600
Sequence in context: A103927 A103928 A103929 this_sequence A000712 A032442 A102688
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 09 2006
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