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Search: id:A093160
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| A093160 |
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Expansion of q^(-1/2)* (eta(q^4)/ eta(q))^4 in powers of q. |
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+0
3
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| 1, 4, 14, 40, 101, 236, 518, 1080, 2162, 4180, 7840, 14328, 25591, 44776, 76918, 129952, 216240, 354864, 574958, 920600, 1457946, 2285452, 3548550, 5460592, 8332425, 12614088, 18953310, 28276968, 41904208, 61702876, 90304598
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OFFSET
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0,2
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FORMULA
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Euler transform of period 4 sequence [4, 4, 4, 0, ...].
G.f.: (Product_{n>0} (1+x^(2n))/ (1-x^(2n-1)))^4.
Given g.f. A(x), then B(x)= x*A(x^2) 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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PROGRAM
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(PARI) {a(n)= if(n<0, 0, polcoeff( (eta(x^4+x*O(x^n))/ eta(x+x*O(x^n)))^4, n))}
(PARI) {a(n)= local(A, A2, m); if(n<0, 0, A= x+O(x^2); m=1; while(m<=n, m*=2; A= subst(A, x, x^2); A2= A*(1+16*A); A= 8*A2+(1+32*A)* sqrt(A2)); polcoeff(sqrt(A/x), n))}
(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( (eta(x^4+A)/ eta(x+A))^4, n))}
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CROSSREFS
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A001938(n) = (-1)^n* a(n).
Sequence in context: A074083 A144141 A066375 this_sequence A001938 A066368 A121593
Adjacent sequences: A093157 A093158 A093159 this_sequence A093161 A093162 A093163
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos Mar 26 2004, Apr 17 2007
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