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The Riordan square of the permutation involutions. Triangle T(n, k), 0 <= k <= n, read by rows.
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%I #4 Dec 09 2018 12:32:40

%S 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,

%T 11,1,232,568,630,462,228,72,13,1,764,1840,2072,1644,938,374,98,15,1,

%U 2620,6204,6972,5788,3650,1710,572,128,17,1

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

%C The Riordan square is defined in A321620.

%e [0] 1;

%e [1] 1, 1;

%e [2] 2, 3, 1;

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

%e [4] 10, 22, 18, 7, 1;

%e [5] 26, 62, 60, 32, 9, 1;

%e [6] 76, 184, 194, 126, 50, 11, 1;

%e [7] 232, 568, 630, 462, 228, 72, 13, 1;

%e [8] 764, 1840, 2072, 1644, 938, 374, 98, 15, 1;

%e [9] 2620, 6204, 6972, 5788, 3650, 1710, 572, 128, 17, 1;

%p # The function RiordanSquare is defined in A321620.

%p cf := proc(dim) local k, m; m := 1;

%p for k from dim by -1 to 1 do m := 1 - k*x - k*x^2/m od;

%p 1/m end: RiordanSquare(cf(9), 9);

%Y First column are the self-inverse permutations A000085.

%Y Row sums are A193777, alternating row sums are A000007.

%Y Cf. A321620.

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, Dec 09 2018