|
%I #17 Dec 20 2022 04:43:54
%S 3,3,3,12,3,3,25,25,3,3,42,90,42,3,3,63,231,231,63,3,3,88,490,840,490,
%T 88,3,3,117,918,2394,2394,918,117,3,3,150,1575,5796,8820,5796,1575,
%U 150,3,3,187,2530,12474,26796,26796,12474,2530,187,3
%N Let k=1; then T(n,m) = (((2*k+1)/(m+k+1))*binomial(n-1-k, m-k)*binomial(n+k, m+k) + ((2*k+1)/(n-m+k))*binomial(n-1-k, n-m-1-k)*binomial(n+k, n-m-1+k)), irregular triangle.
%e {3, 3},
%e {3, 12, 3},
%e {3, 25, 25, 3},
%e {3, 42, 90, 42, 3},
%e {3, 63, 231, 231, 63, 3},
%e {3, 88, 490, 840, 490, 88, 3},
%e {3, 117, 918, 2394, 2394, 918, 117, 3},
%e {3, 150, 1575, 5796, 8820, 5796, 1575, 150, 3},
%e {3, 187, 2530, 12474, 26796, 26796, 12474, 2530, 187, 3}
%t With[{k = 1}, Table[(((2 k + 1)/(m + k + 1))*Binomial[n - 1 - k, m - k] * Binomial[n + k, m + k] + ((2 k + 1)/(n - m + k))*Binomial[n - 1 - k, n - m - 1 - k] * Binomial[n + k, n - m - 1 + k]), {n, k + 1, 10}, {m, 0, n - 1}]] // Flatten (* _Michael De Vlieger_, Dec 19 2022 *)
%Y Cf. A156716.
%K nonn,tabf,less
%O 0,1
%A _Roger L. Bagula_, Feb 14 2009
|
