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A321623 The Riordan square of the large Schröder numbers, triangle read by rows, T(n, k) for 0 <= k <= n. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

LINKS

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

FORMULA

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

EXAMPLE

[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]

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 *)

PROG

(Sage) # uses[riordan_square from A321620]

riordan_square((1 - x - sqrt(1 - 6*x + x^2))/(2*x), 10)

CROSSREFS

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

Cf. A321620, A133367.

Sequence in context: A192659 A327485 A207975 * A077063 A081728 A197218

Adjacent sequences: A321620 A321621 A321622 * A321624 A321625 A321626

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Nov 22 2018

STATUS

approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)