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

0,4

Comments

The Riordan square is defined in A321620.

Links

Table of n, a(n) for n=0..54.

Example

[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;

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);

Crossrefs

First column are the self-inverse permutations A000085.

Row sums are A193777, alternating row sums are A000007.

Cf. A321620.

Sequence in context: A118800 A200139 A321621 * A353594 A075297 A057597

Adjacent sequences: A321626 A321627 A321628 * A321630 A321631 A321632

Keyword

nonn,tabl

Author

Peter Luschny, Dec 09 2018

Status

approved