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

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, 17, 1, 264, 1056, 1722, 1470, 700, 182, 23, 1, 858, 3861, 7260, 7392, 4410, 1554, 308, 30, 1, 2860, 14300, 30459, 36036, 25872, 11550, 3150, 492, 38, 1

Offset: 0

Author

Peter Luschny, May 02 2022

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0]    1;
[1]    1,     1;
[2]    2,     3,     1;
[3]    4,     8,     5,     1;
[4]   10,    25,    22,     8,     1;
[5]   28,    84,    95,    50,    12,     1;
[6]   84,   294,   406,   280,   100,    17,    1;
[7]  264,  1056,  1722,  1470,   700,   182,   23,   1;
[8]  858,  3861,  7260,  7392,  4410,  1554,  308,  30,  1;
[9] 2860, 14300, 30459, 36036, 25872, 11550, 3150, 492, 38, 1;
		

Crossrefs

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

Programs

Maple

S := (n, k) -> if n = k then 1 elif k = 0 then 0 else
binomial(n, k)^2*(k*(2*k^2 + (n + 1)*(n - 2*k)))/(n^2*(n - 1)*(n - k + 1)) fi:
T := (n, k) -> add(binomial(j, k)*S(n, j), j = 0..n):