

A081265


Triangle of coefficients of the polynomials a(n, x) = 2*a(n1, x)+ x^2*a(n2,x), n >= 1, a(0, x) = 1, a(1, x) = 1.


2



1, 1, 0, 2, 0, 1, 4, 0, 3, 0, 8, 0, 8, 0, 1, 16, 0, 20, 0, 5, 0, 32, 0, 48, 0, 18, 0, 1, 64, 0, 112, 0, 56, 0, 7, 0, 128, 0, 256, 0, 160, 0, 32, 0, 1, 256, 0, 576, 0, 432, 0, 120, 0, 9, 0, 512, 0, 1280, 0, 1120, 0, 400, 0, 50, 0, 1, 1024, 0, 2816, 0, 2816, 0, 1232, 0, 220
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OFFSET

0,4


COMMENTS

Unsigned Chebyshev numbers of the first kind. Columns include A011782, A001792, A001793, A001794, A006974.
For the Riordan coefficient triangle for Chebyshev's Tpolynomials (decreasing odd or even powers of x) see A039991.  Wolfdieter Lang, Aug 06 2014


LINKS

Table of n, a(n) for n=0..74.


FORMULA

T(n,k) = [x^k] a(n,x), k = 0, 1, ..., n, with polynomial a(n,x) defined by the recurrence given as name. Its Binetde Moivre form is a(n, x) = ((1+sqrt(x^2+1))^n + (1sqrt(x^2+1))^n)/2.
O.g.f. for row polynomials a(n,x): (1z)/(1  2*z  (x*z)^2). Compare with A039991.


EXAMPLE

Triangle rows are {1}, {1,0}, {2,0,1}, {4,0,3,0}, {8,0,8,0,1},.... [Corrected by Philippe Deléham, Dec 27 2007]
See the unsigned example under A039991.  Wolfdieter Lang, Aug 06 2014


CROSSREFS

Cf. A008310, A039991 (signed).
Sequence in context: A341101 A342909 A039991 * A273821 A108643 A133838
Adjacent sequences: A081262 A081263 A081264 * A081266 A081267 A081268


KEYWORD

easy,nonn,tabl


AUTHOR

Paul Barry, Mar 15 2003


EXTENSIONS

Edited. Name and formula clarified. G.f. of row polynomial, and crossref. A039991 added.  Wolfdieter Lang, Aug 06 2014


STATUS

approved



