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A108045
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Triangle read by rows: lower triangular matrix obtained by inverting the lower triangular matrix in A108044.
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3
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1, 0, 1, -2, 0, 1, 0, -3, 0, 1, 2, 0, -4, 0, 1, 0, 5, 0, -5, 0, 1, -2, 0, 9, 0, -6, 0, 1, 0, -7, 0, 14, 0, -7, 0, 1, 2, 0, -16, 0, 20, 0, -8, 0, 1, 0, 9, 0, -30, 0, 27, 0, -9, 0, 1, -2, 0, 25, 0, -50, 0, 35, 0, -10, 0, 1, 0, -11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1, 2, 0, -36, 0, 105, 0, -112, 0, 54, 0, -12, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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This triangle describes the Chebyshev transform of A100047 and following. Chebyshev transform of sequence b is c(n) = SUM (a(n,k)*b(k), k=1 to n). - Christian G. Bower, Jun 12 2005
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REFERENCES
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Aoife Hennessy, A Study of Riordan Arrays with Applications to Continued Fractions, Orthogonal Polynomials and Lattice Paths, Ph. D. Thesis, Waterford Institute of Technology, Oct. 2011; http://repository.wit.ie/1693/1/AoifeThesis.pdf
L. W. Shapiro, S. Getu, W.-J. Woan and L. C. Woodson, The Riordan group, Discrete Applied Math., 34 (1991), 229-239.
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LINKS
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Table of n, a(n) for n=0..90.
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FORMULA
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Riordan array ( (1-x^2)/(1+x^2), x/(1+x^2)).
G.f.=(1-x^2)/(1+x^2-tx). - Emeric Deutsch, Jun 06 2005
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EXAMPLE
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Triangle begins:
.1
.0 1
.-2 0 1
.0 -3 0 1
.2 0 -4 0 1
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MAPLE
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f:=(1-x^2)/(1+x^2): g:=x/(1+x^2): G:=simplify(f/(1-t*g)): Gser:=simplify(series(G, x=0, 14)): P[0]:=1: for n from 1 to 12 do P[n]:=coeff(Gser, x^n) od: for n from 0 to 12 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form (Deutsch)
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CROSSREFS
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Cf. A007318, A108044.
Cf. A127672.
Sequence in context: A053119 A162515 A175267 * A143728 A127368 A112552
Adjacent sequences: A108042 A108043 A108044 * A108046 A108047 A108048
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KEYWORD
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sign,tabl,easy
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AUTHOR
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N. J. A. Sloane, Jun 02 2005
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EXTENSIONS
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More terms from Emeric Deutsch and Christian G. Bower, Jun 06 2005
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STATUS
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approved
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