The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101124 Number triangle associated to Chebyshev polynomials of first kind. 7
1, 0, 1, -1, 1, 1, 0, 1, 2, 1, 1, 1, 7, 3, 1, 0, 1, 26, 17, 4, 1, -1, 1, 97, 99, 31, 5, 1, 0, 1, 362, 577, 244, 49, 6, 1, 1, 1, 1351, 3363, 1921, 485, 71, 7, 1, 0, 1, 5042, 19601, 15124, 4801, 846, 97, 8, 1, -1, 1, 18817, 114243, 119071, 47525, 10081, 1351, 127, 9, 1, 0, 1, 70226, 665857, 937444, 470449, 120126, 18817, 2024, 161 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
FORMULA
Number triangle S(n, k)=T(n-k, k), k<n, S(n, n)=1, 0 otherwise, where T(n, k)=(n/2)sum{j=0..floor(n/2), C(n-j, j)(-1)^j*(2k)^(n-2j)}.
Columns have g.f. x^k(1-kx)/(1-2kx+x^2).
Also, square array if(n=0, 1, T(n, k)) read by antidiagonals.
EXAMPLE
As a number triangle, rows begin:
{1},
{0,1},
{-1,1,1},
{0,1,2,1},
...
As a square array, rows begin
1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, ...
-1, 1, 7, 17, 31, ...
0, 1, 26, 99, 244, ...
1, 1, 97, 577, 1921, ...
MATHEMATICA
T[n_, k_] := SeriesCoefficient[x^k (1 - k x)/(1 - 2 k x + x^2), {x, 0, n}];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 12 2017 *)
CROSSREFS
Row sums are A101125.
Diagonal sums are A101126.
Main diagonal gives A115066.
Mirror of A322836.
Cf. A053120.
Sequence in context: A137296 A329291 A294105 * A011127 A172970 A172971
KEYWORD
easy,sign,tabl
AUTHOR
Paul Barry, Dec 02 2004
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 07:40 EDT 2024. Contains 373469 sequences. (Running on oeis4.)