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URL: https://oeis.org/A101161

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A101161
A number triangle associated with the Chebyshev polynomials of the first kind.
2
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.
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: A263703 A263752 A391726 * A245049 A214261 A097825
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Dec 02 2004
STATUS
approved