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