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%I #16 Feb 17 2020 11:37:36
%S 1,1,1,3,4,1,15,21,7,1,105,144,48,10,1,945,1245,372,84,13,1,10395,
%T 13140,3357,726,129,16,1,135135,164745,35415,6873,1233,183,19,1,
%U 2027025,2399040,434520,73116,12306,1920,246,22,1
%N The Riordan square of the double factorial of odd numbers. Triangle T(n, k), 0 <= k <= n, read by rows.
%C The Riordan square is defined in A321620.
%C Triangle, read by rows, given by [1, 2, 3, 4, 5, 6, 7, …] DELTA [1, 0, 0, 0, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Feb 17 2020
%e Triangle starts:
%e [0][ 1]
%e [1][ 1, 1]
%e [2][ 3, 4, 1]
%e [3][ 15, 21, 7, 1]
%e [4][ 105, 144, 48, 10, 1]
%e [5][ 945, 1245, 372, 84, 13, 1]
%e [6][ 10395, 13140, 3357, 726, 129, 16, 1]
%e [7][135135, 164745, 35415, 6873, 1233, 183, 19, 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/m od;
%p 1/m end: RiordanSquare(cf(9), 9);
%t (* The function RiordanSquare is defined in A321620. *)
%t cf[dim_] := Module[{k, m=1}, For[k=dim, k >= 1, k--, m = 1 - k*x/m]; 1/m];
%t RiordanSquare[cf[9], 9] (* _Jean-François Alcover_, Jun 15 2019, from Maple *)
%Y First column are the double factorial of odd numbers A001147.
%Y Second column is number of singletons in pair-partitions A233481.
%Y Row sums are A321628, alternating row sums are A000007.
%Y Cf. A321620.
%K nonn,tabl
%O 0,4
%A _Peter Luschny_, Dec 07 2018
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