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Triangle read by rows, T(n, k) = Sum_{j=0..n} binomial(j, k)*A352687(n, j).
0

%I #5 Jul 30 2023 17:44:37

%S 1,1,1,2,3,1,4,8,5,1,10,25,22,8,1,28,84,95,50,12,1,84,294,406,280,100,

%T 17,1,264,1056,1722,1470,700,182,23,1,858,3861,7260,7392,4410,1554,

%U 308,30,1,2860,14300,30459,36036,25872,11550,3150,492,38,1

%N Triangle read by rows, T(n, k) = Sum_{j=0..n} binomial(j, k)*A352687(n, j).

%e Triangle starts:

%e [0] 1;

%e [1] 1, 1;

%e [2] 2, 3, 1;

%e [3] 4, 8, 5, 1;

%e [4] 10, 25, 22, 8, 1;

%e [5] 28, 84, 95, 50, 12, 1;

%e [6] 84, 294, 406, 280, 100, 17, 1;

%e [7] 264, 1056, 1722, 1470, 700, 182, 23, 1;

%e [8] 858, 3861, 7260, 7392, 4410, 1554, 308, 30, 1;

%e [9] 2860, 14300, 30459, 36036, 25872, 11550, 3150, 492, 38, 1;

%p S := (n, k) -> if n = k then 1 elif k = 0 then 0 else

%p binomial(n, k)^2*(k*(2*k^2 + (n + 1)*(n - 2*k)))/(n^2*(n - 1)*(n - k + 1)) fi:

%p T := (n, k) -> add(binomial(j, k)*S(n, j), j = 0..n):

%Y Cf. A352687, A068875 (column 0), A238113 (half row sums)

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, May 02 2022