|
%I #12 Jan 25 2019 04:10:26
%S 2,3,3,4,10,4,5,31,31,5,6,102,182,102,6,7,367,1093,1093,367,7,8,1402,
%T 8032,8738,8032,1402,8,9,5511,67763,86181,86181,67763,5511,9,10,21910,
%U 600322,1166470,813802,1166470,600322,21910,10,11,87463,5385001,18015797,11900131,11900131,18015797,5385001,87463,11
%N T(n, k) = k^n*U(n, (1/k + k)/2) + (n + 1)^(k - 1)*U(k - 1, (1/(n + 1) + n + 1)/2), where U(n,x) is the n-th Chebyshev polynomial of the second kind, square array read by antidiagonals (n >= 0, k >= 1).
%F T(n,k) = A173588(n,k) + A173588(k-1,n+1).
%e Square array begins:
%e n\k | 1 2 3 4 5 6 ...
%e -----------------------------------------------------
%e 0 | 2 3 4 5 6 7 ...
%e 1 | 3 10 31 102 367 1402 ...
%e 2 | 4 31 182 1093 8032 67763 ...
%e 3 | 5 102 1093 8738 86181 1166470 ...
%e 4 | 6 367 8032 86181 813802 11900131 ...
%e 5 | 7 1402 67763 1166470 11900131 124387562 ...
%e 6 | 8 5511 600322 18015797 260198052 2527336267 ...
%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 b = (a + Transpose[a]);
%t Flatten[Table[Table[b[[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) + (n + 1)^(k - 1)*chebyshev_u(k - 1, (1/(n + 1) + n + 1)/2)$
%o create_list(T(n - k + 1, k), n, 0, 12, k, 1, n + 1);
%o /* _Franck Maminirina Ramaharo_, Jan 24 2019 */
%Y Cf. A173588, A173591.
%K nonn,easy,tabl
%O 0,1
%A _Roger L. Bagula_, Feb 22 2010
%E Edited by _Franck Maminirina Ramaharo_, Jan 24 2019
|
