Search: id:A099451
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%I A099451
%S A099451 1,5,17,45,96,155,119,365,2217,7360,18791,38435,57639,28875,200992,1015075,
%T A099451 3179711,7796715,15240559,20915840,3218033,103746315,458355231,1362884995,
%U A099451 3211177504,5977952405,7345234233,2382397955,51340513351,204512766400,
               579756435849
%V A099451 1,5,17,45,96,155,119,-365,-2217,-7360,-18791,-38435,-57639,-28875,200992,
               1015075,
%W A099451 3179711,7796715,15240559,20915840,3218033,-103746315,-458355231,-1362884995,
%X A099451 -3211177504,-5977952405,-7345234233,2382397955,51340513351,204512766400,
               579756435849
%N A099451 A Chebyshev transform of A099450 associated to the knot 7_7.
%C A099451 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)).
%H A099451 Dror Bar-Natan, <a href="http://www.math.toronto.edu/~drorbn/KAtlas/Knots/
               ">The Rolfsen Knot Table</a>
%F A099451 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}.
%Y A099451 Sequence in context: A146858 A146183 A163424 this_sequence A133252 A048612 
               A147050
%Y A099451 Adjacent sequences: A099448 A099449 A099450 this_sequence A099452 A099453 
               A099454
%K A099451 easy,sign
%O A099451 0,2
%A A099451 Paul Barry (pbarry(AT)wit.ie), Oct 16 2004

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