A173588 T(n,k) = (k^n)*U(n, (1/k + k)/2), where U(n,x) is the n-th Chebyshev polynomial of the second kind, square array read by antidiagonals upward (n >= 0, k >= 1).

1, 2, 1, 3, 5, 1, 4, 21, 10, 1, 5, 85, 91, 17, 1, 6, 341, 820, 273, 26, 1, 7, 1365, 7381, 4369, 651, 37, 1, 8, 5461, 66430, 69905, 16276, 1333, 50, 1, 9, 21845, 597871, 1118481, 406901, 47989, 2451, 65, 1, 10, 87381, 5380840, 17895697, 10172526, 1727605, 120100, 4161, 82, 1

Offset

0,2

Comments

The intersection of this sequence and A121290 is the sequence 1, 5, 85, 341, 5461, 21845, .... - Paul Muljadi, Jan 27 2011

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = (k^n)*([x^n] 1/(x^2 - (1/k + k)*x + 1)).

Example

Square array begins:
  n\k | 1    2      3        4         5          6 ...
  -----------------------------------------------------
   0  | 1    1      1        1         1          1 ...
   1  | 2    5     10       17        26         37 ...
   2  | 3   21     91      273       651       1333 ...
   3  | 4   85    820     4369     16276      47989 ...
   4  | 5  341   7381    69905    406901    1727605 ...
   5  | 6 1365  66430  1118481  10172526   62193781 ...
   6  | 7 5461 597871 17895697 254313151 2238976117 ...
   ...

Mathematica

p[x_, q_] = 1/(x^2 - (1/q + q)*x + 1);
a = Table[Table[n^m*SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], {m, 0, 20}], {n, 1, 21}];
Flatten[Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]]

Prog

(Maxima)
T(n, k) := k^n*chebyshev_u(n, (1/k + k)/2)$
create_list(T(n - k + 1, k), n, 0, 12, k, 1, n + 1);
/* Franck Maminirina Ramaharo, Jan 18 2019 */

Crossrefs

Cf. A001045, A002450.

Cf. A173590, A173591.

Sequence in context: A202179 A297519 A297749 * A286942 A125076 A220562

Adjacent sequences: A173585 A173586 A173587 * A173589 A173590 A173591

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Feb 22 2010

Extensions

Edited by Franck Maminirina Ramaharo, Jan 24 2019

Status

approved