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A132136
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Expansion of -lambda(t+1) in powers of nome q = exp(pi i t).
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0
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16, 128, 704, 3072, 11488, 38400, 117632, 335872, 904784, 2320128, 5702208, 13504512, 30952544, 68901888, 149403264, 316342272, 655445792, 1331327616, 2655115712, 5206288384, 10049485312, 19115905536, 35867019904, 66437873664
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Eric Weisstein's World of Mathematics, Elliptic Lambda Function
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FORMULA
| Expansion of lambda(t)/( 1-lambda(t)) in powers of nome q = exp(pi i t).
Expansion of 16* (eta(q^4)/ eta(q))^8 in powers of q.
G.f.: 16*x* (Product_{k>0} (1+x^(2k))/ (1-x^(2k-1)))^8.
Given G.f. A(x), then B(x)= A(x)/16 satisfies 0= f(B(x), B(x^2)) where f(u, v)= u^2 -v -16*u*v -16*v^2 -256*u*v^2.
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PROG
| (PARI) {a(n)= local(A); if(n<1, 0, n--; A=x*O(x^n); 16*polcoeff( (eta(x^4+A)/eta(x+A))^8, n))}
(PARI) {a(n)= local(A); if(n<1, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)^3/eta(x+A)^2/eta(x^4+A))^8, n))}
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CROSSREFS
| 16*A092877(n)= a(n). A115977(n)= -(-1)^n*a(n). A014972(n)= a(n) unless n=0.
Sequence in context: A014972 A115977 A128692 * A163399 A067488 A120785
Adjacent sequences: A132133 A132134 A132135 * A132137 A132138 A132139
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 11 2007
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