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Search: id:A115066
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| A115066 |
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Chebyshev polynomial of the first kind T(n,x), evaluated at x=n. |
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+0
2
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| 1, 1, 7, 99, 1921, 47525, 1431431, 50843527, 2081028097, 96450076809, 4993116004999, 285573847759211, 17882714781360001, 1216895030905226413, 89415396036432386311, 7055673735003659189775, 595077930963909484707841
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Rosenblum and Rovnyak, Hardy Classes and Operator Theory,Dover, New York,1985, page 18
G. Szego, Orthogonal polynomials, Amer. Math. Soc., Providence, 1939, p. 29.
G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1966, p. 35.
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FORMULA
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a(n)=cos(n*arccos(n)).
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EXAMPLE
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a(3)=99 because T[3,x]=4x^3-3x and T[3,3]=4*3^3-3*3=99.
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MAPLE
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with(orthopoly): seq(T(n, n), n=0..17);
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CROSSREFS
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Sequence in context: A092818 A041087 A041084 this_sequence A123616 A001594 A052752
Adjacent sequences: A115063 A115064 A115065 this_sequence A115067 A115068 A115069
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 01 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 05 2006
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