A321623 The Riordan square of the large Schröder numbers, triangle read by rows, T(n, k) for 0 <= k <= n.

1, 2, 2, 6, 10, 4, 22, 46, 32, 8, 90, 214, 196, 88, 16, 394, 1018, 1104, 672, 224, 32, 1806, 4946, 6020, 4448, 2048, 544, 64, 8558, 24470, 32400, 27432, 15584, 5792, 1280, 128, 41586, 122926, 173572, 162680, 107408, 49824, 15552, 2944, 256

Offset: 0

Author

Peter Luschny, Nov 22 2018

Keywords

• nonn
• tabl

Comments

Triangle, read by rows,given by [2,1,2,1,2,1,2,1,...]DELTA[2,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 05 2020

Examples

			[0][     1]
[1][     2,      2]
[2][     6,     10,      4]
[3][    22,     46,     32,      8]
[4][    90,    214,    196,     88,     16]
[5][   394,   1018,   1104,    672,    224,     32]
[6][  1806,   4946,   6020,   4448,   2048,    544,     64]
[7][  8558,  24470,  32400,  27432,  15584,   5792,   1280,   128]
[8][ 41586, 122926, 173572, 162680, 107408,  49824,  15552,  2944,  256]
[9][206098, 625522, 929248, 942592, 697408, 379840, 149248, 40192, 6656, 512]
		

Crossrefs

T(n, 0) = A006318 (large Schröder), A321574 (row sums), A000007 (alternating row sums).

Cf. A321620, A133367.

Programs

Maple

# The function RiordanSquare is defined in A321620.
LargeSchröder := x -> (1 - x - sqrt(1 - 6*x + x^2))/(2*x);
RiordanSquare(LargeSchröder(x), 10);

Mathematica

(* The function RiordanSquare is defined in A321620. *)
LargeSchröder[x_] := (1 - x - Sqrt[1 - 6*x + x^2])/(2*x);
RiordanSquare[LargeSchröder[x], 10] (* Jean-François Alcover, Jun 15 2019, from Maple *)

Sage

# uses[riordan_square from A321620]
riordan_square((1 - x - sqrt(1 - 6*x + x^2))/(2*x), 10)

Formula

T(n, k) = 2^k*A133367(n,k). - Philippe Deléham, Feb 05 2020