A321629 The Riordan square of the permutation involutions. Triangle T(n, k), 0 <= k <= n, read by rows.

1, 1, 1, 2, 3, 1, 4, 8, 5, 1, 10, 22, 18, 7, 1, 26, 62, 60, 32, 9, 1, 76, 184, 194, 126, 50, 11, 1, 232, 568, 630, 462, 228, 72, 13, 1, 764, 1840, 2072, 1644, 938, 374, 98, 15, 1, 2620, 6204, 6972, 5788, 3650, 1710, 572, 128, 17, 1

Offset: 0

Author

Peter Luschny, Dec 09 2018

Keywords

• nonn
• tabl

Comments

The Riordan square is defined in A321620.

Examples

			[0]    1;
[1]    1,    1;
[2]    2,    3,    1;
[3]    4,    8,    5,    1;
[4]   10,   22,   18,    7,    1;
[5]   26,   62,   60,   32,    9,    1;
[6]   76,  184,  194,  126,   50,   11,   1;
[7]  232,  568,  630,  462,  228,   72,  13,   1;
[8]  764, 1840, 2072, 1644,  938,  374,  98,  15,  1;
[9] 2620, 6204, 6972, 5788, 3650, 1710, 572, 128, 17, 1;
		

Crossrefs

First column are the self-inverse permutations A000085.

Row sums are A193777, alternating row sums are A000007.

Cf. A321620.

Programs

Maple

# The function RiordanSquare is defined in A321620.
cf := proc(dim) local k, m; m := 1;
for k from dim by -1 to 1 do m := 1 - k*x - k*x^2/m od;
1/m end: RiordanSquare(cf(9), 9);