A101161 A number triangle associated with the Chebyshev polynomials of the first kind.

1, 2, 1, 2, 3, 1, 2, 7, 4, 1, 2, 18, 14, 5, 1, 2, 47, 52, 23, 6, 1, 2, 123, 194, 110, 34, 7, 1, 2, 322, 724, 527, 198, 47, 8, 1, 2, 843, 2702, 2525, 1154, 322, 62, 9, 1, 2, 2207, 10084, 12098, 6726, 2207, 488, 79, 10, 1, 2, 5778, 37634, 57965, 39202, 15127, 3842, 702, 98

Offset

0,2

Comments

Row sums are A101162. Diagonal sums are A101163.

Links

Table of n, a(n) for n=0..63.

Index entries for sequences related to Chebyshev polynomials.

Formula

Number triangle S(n, k)=if(n=k, 1, 2T(n-k, (k+2)/2)) where T(n, k)=(n/2)*Sum_{j=0..floor(n/2)} C(n-j, j)(-1)^j*(2k)^(n-2j).

Number triangle S(n, k) = if(k<n, Sum_{j=0..n} C(n-k+j, 2*j)*(2*(n-k)/(n-k+j))*k^j, if(k=n, 1, 0)).

Columns have g.f. (1-x^2)*x^k/(1-(k+2)*x+x^2).

Square array if(n=0, 1, 2T(n, (k+2)/2) read by antidiagonals.

Example

Rows begin:
  {1},
  {2,1},
  {2,3,1},
  {2,7,4,1},
  {2,18,14,5,1},
  ...
As a square array, rows begin:
  1,1,1,1,1,...
  2,3,4,5,6,...
  2,7,14,23,34,...
  2,18,52,110,198,...
  2,47,194,527,1154,...

Crossrefs

Sequence in context: A263714 A263703 A263752 * A245049 A214261 A097825

Adjacent sequences: A101158 A101159 A101160 * A101162 A101163 A101164

Keyword

easy,nonn,tabl

Author

Paul Barry, Dec 02 2004

Status

approved