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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).

%I A173588 #17 Jan 25 2019 04:09:55
%S A173588 1,2,1,3,5,1,4,21,10,1,5,85,91,17,1,6,341,820,273,26,1,7,1365,7381,
%T A173588 4369,651,37,1,8,5461,66430,69905,16276,1333,50,1,9,21845,597871,
%U A173588 1118481,406901,47989,2451,65,1,10,87381,5380840,17895697,10172526,1727605,120100,4161,82,1
%N 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).
%C A173588 The intersection of this sequence and A121290 is the sequence 1, 5, 85, 341, 5461, 21845, .... - _Paul Muljadi_, Jan 27 2011
%F A173588 T(n,k) = (k^n)*([x^n] 1/(x^2 - (1/k + k)*x + 1)).
%e A173588 Square array begins:
%e A173588   n\k | 1    2      3        4         5          6 ...
%e A173588   -----------------------------------------------------
%e A173588    0  | 1    1      1        1         1          1 ...
%e A173588    1  | 2    5     10       17        26         37 ...
%e A173588    2  | 3   21     91      273       651       1333 ...
%e A173588    3  | 4   85    820     4369     16276      47989 ...
%e A173588    4  | 5  341   7381    69905    406901    1727605 ...
%e A173588    5  | 6 1365  66430  1118481  10172526   62193781 ...
%e A173588    6  | 7 5461 597871 17895697 254313151 2238976117 ...
%e A173588    ...
%t A173588 p[x_, q_] = 1/(x^2 - (1/q + q)*x + 1);
%t A173588 a = Table[Table[n^m*SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], {m, 0, 20}], {n, 1, 21}];
%t A173588 Flatten[Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]]
%o A173588 (Maxima)
%o A173588 T(n, k) := k^n*chebyshev_u(n, (1/k + k)/2)$
%o A173588 create_list(T(n - k + 1, k), n, 0, 12, k, 1, n + 1);
%o A173588 /* _Franck Maminirina Ramaharo_, Jan 18 2019 */
%Y A173588 Cf. A001045, A002450.
%Y A173588 Cf. A173590, A173591.
%K A173588 nonn,easy,tabl
%O A173588 0,2
%A A173588 _Roger L. Bagula_, Feb 22 2010
%E A173588 Edited by _Franck Maminirina Ramaharo_, Jan 24 2019