A321627 The Riordan square of the double factorial of odd numbers. Triangle T(n, k), 0 <= k <= n, read by rows.

1, 1, 1, 3, 4, 1, 15, 21, 7, 1, 105, 144, 48, 10, 1, 945, 1245, 372, 84, 13, 1, 10395, 13140, 3357, 726, 129, 16, 1, 135135, 164745, 35415, 6873, 1233, 183, 19, 1, 2027025, 2399040, 434520, 73116, 12306, 1920, 246, 22, 1

Offset

0,4

Comments

The Riordan square is defined in A321620.

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

Links

Table of n, a(n) for n=0..44.

Example

Triangle starts:
[0][     1]
[1][     1,      1]
[2][     3,      4,     1]
[3][    15,     21,     7,    1]
[4][   105,    144,    48,   10,    1]
[5][   945,   1245,   372,   84,   13,   1]
[6][ 10395,  13140,  3357,  726,  129,  16,  1]
[7][135135, 164745, 35415, 6873, 1233, 183, 19, 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/m od;
1/m end: RiordanSquare(cf(9), 9);

Mathematica

(* The function RiordanSquare is defined in A321620. *)
cf[dim_] := Module[{k, m=1}, For[k=dim, k >= 1, k--, m = 1 - k*x/m]; 1/m];
RiordanSquare[cf[9], 9] (* Jean-François Alcover, Jun 15 2019, from Maple *)

Crossrefs

First column are the double factorial of odd numbers A001147.

Second column is number of singletons in pair-partitions A233481.

Row sums are A321628, alternating row sums are A000007.

Cf. A321620.

Sequence in context: A059110 A100326 A303728 * A350557 A028338 A039757

Adjacent sequences: A321624 A321625 A321626 * A321628 A321629 A321630

Keyword

nonn,tabl

Author

Peter Luschny, Dec 07 2018

Status

approved