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A099451
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A Chebyshev transform of A099450 associated to the knot 7_7.
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2
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1, 5, 17, 45, 96, 155, 119, -365, -2217, -7360, -18791, -38435, -57639, -28875, 200992, 1015075, 3179711, 7796715, 15240559, 20915840, 3218033, -103746315, -458355231, -1362884995, -3211177504, -5977952405, -7345234233, 2382397955, 51340513351, 204512766400, 579756435849
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The denominator is a parameterisation of the Alexander polynomial for the knot 7_7. The g.f. is the image of the g.f. of A099450 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
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LINKS
| Dror Bar-Natan, The Rolfsen Knot Table
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FORMULA
| G.f.: (1+x^2)/(1-5x+9x^2-5x^3+x^4); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-2k, C(n-2k-j, j)(-7)^j*5^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A099450(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A099450(k)/2}; a(n)=sum{k=0..n, A099452(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.
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CROSSREFS
| Sequence in context: A146183 A163424 A190969 * A174794 A133252 A048612
Adjacent sequences: A099448 A099449 A099450 * A099452 A099453 A099454
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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