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A353594 Triangle read by rows, T(n, k) = Sum_{j=0..n} binomial(j, k)*A352687(n, j).

%I A353594 #5 Jul 30 2023 17:44:37
%S A353594 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 A353594 17,1,264,1056,1722,1470,700,182,23,1,858,3861,7260,7392,4410,1554,
%U A353594 308,30,1,2860,14300,30459,36036,25872,11550,3150,492,38,1
%N A353594 Triangle read by rows, T(n, k) = Sum_{j=0..n} binomial(j, k)*A352687(n, j).
%e A353594 Triangle starts:
%e A353594 [0]    1;
%e A353594 [1]    1,     1;
%e A353594 [2]    2,     3,     1;
%e A353594 [3]    4,     8,     5,     1;
%e A353594 [4]   10,    25,    22,     8,     1;
%e A353594 [5]   28,    84,    95,    50,    12,     1;
%e A353594 [6]   84,   294,   406,   280,   100,    17,    1;
%e A353594 [7]  264,  1056,  1722,  1470,   700,   182,   23,   1;
%e A353594 [8]  858,  3861,  7260,  7392,  4410,  1554,  308,  30,  1;
%e A353594 [9] 2860, 14300, 30459, 36036, 25872, 11550, 3150, 492, 38, 1;
%p A353594 S := (n, k) -> if n = k then 1 elif k = 0 then 0 else
%p A353594 binomial(n, k)^2*(k*(2*k^2 + (n + 1)*(n - 2*k)))/(n^2*(n - 1)*(n - k + 1)) fi:
%p A353594 T := (n, k) -> add(binomial(j, k)*S(n, j), j = 0..n):
%Y A353594 Cf. A352687, A068875 (column 0), A238113 (half row sums)
%K A353594 nonn,tabl
%O A353594 0,4
%A A353594 _Peter Luschny_, May 02 2022