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Search: id:A164660
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| A164660 |
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Numerators of row sums of triangle of rationals A164658/A164659. Definite integral of Chebyshev's polynomials of the first kind: int(T(n,x),x=0..1). |
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6
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| 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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W. Lang: First ten rows of the rational table.
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)=numerator(sum(IT(n,m),m=1..n+1)), n>=0, with IT(n,m):= A164658(n,m)/A164659(n,m) (coefficient triangle from the indefinite integral int(T(n,x),x), n>=0, in lowest terms).
Conjecture for the rationals r(n):= A164660(n)/A164661(n): r(n)= 1 if n=0, if n is even r(n)= -1/((n-1)*(n+1)) and if n is odd r(n)=((-1)^((n-1)/2))/(2*(2*floor((n-1)/4)+1)).
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EXAMPLE
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Rationals a(n)/A164660(n)= [1, 1/2, -1/3, -1/2, -1/15, 1/6, -1/35, -1/6, -1/63, 1/10, -1/99,...].
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CROSSREFS
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The denominators are given in A164661.
Triangle of int(T(n,x),x) coefficients is A164658/A164659.
Sequence in context: A077008 A158387 A087960 this_sequence A114523 A000012 A008836
Adjacent sequences: A164657 A164658 A164659 this_sequence A164661 A164662 A164663
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KEYWORD
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sign,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang@physik.uni-karlsruhe.de) Oct 16 2009
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