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A099451 A Chebyshev transform of A099450 associated to the knot 7_7. 2
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; text; internal format)
OFFSET

0,2

COMMENTS

The denominator is a parameterization 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)).

LINKS

Table of n, a(n) for n=0..30.

Dror Bar-Natan, The Rolfsen Knot Table

Index entries for linear recurrences with constant coefficients, signature (5,-9,5,-1).

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}.

CROSSREFS

Sequence in context: A163424 A294102 A190969 * A174794 A133252 A299335

Adjacent sequences:  A099448 A099449 A099450 * A099452 A099453 A099454

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)