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

%I A321623 #20 Mar 27 2020 17:33:57
%S A321623 1,2,2,6,10,4,22,46,32,8,90,214,196,88,16,394,1018,1104,672,224,32,
%T A321623 1806,4946,6020,4448,2048,544,64,8558,24470,32400,27432,15584,5792,
%U A321623 1280,128,41586,122926,173572,162680,107408,49824,15552,2944,256
%N A321623 The Riordan square of the large Schröder numbers, triangle read by rows, T(n, k) for 0 <= k <= n.
%C A321623 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
%F A321623 T(n, k) = 2^k*A133367(n,k). - _Philippe Deléham_, Feb 05 2020
%e A321623 [0][     1]
%e A321623 [1][     2,      2]
%e A321623 [2][     6,     10,      4]
%e A321623 [3][    22,     46,     32,      8]
%e A321623 [4][    90,    214,    196,     88,     16]
%e A321623 [5][   394,   1018,   1104,    672,    224,     32]
%e A321623 [6][  1806,   4946,   6020,   4448,   2048,    544,     64]
%e A321623 [7][  8558,  24470,  32400,  27432,  15584,   5792,   1280,   128]
%e A321623 [8][ 41586, 122926, 173572, 162680, 107408,  49824,  15552,  2944,  256]
%e A321623 [9][206098, 625522, 929248, 942592, 697408, 379840, 149248, 40192, 6656, 512]
%p A321623 # The function RiordanSquare is defined in A321620.
%p A321623 LargeSchröder := x -> (1 - x - sqrt(1 - 6*x + x^2))/(2*x);
%p A321623 RiordanSquare(LargeSchröder(x), 10);
%t A321623 (* The function RiordanSquare is defined in A321620. *)
%t A321623 LargeSchröder[x_] := (1 - x - Sqrt[1 - 6*x + x^2])/(2*x);
%t A321623 RiordanSquare[LargeSchröder[x], 10] (* _Jean-François Alcover_, Jun 15 2019, from Maple *)
%o A321623 (Sage) # uses[riordan_square from A321620]
%o A321623 riordan_square((1 - x - sqrt(1 - 6*x + x^2))/(2*x), 10)
%Y A321623 T(n, 0) = A006318 (large Schröder), A321574 (row sums), A000007 (alternating row sums).
%Y A321623 Cf. A321620, A133367.
%K A321623 nonn,tabl
%O A321623 0,2
%A A321623 _Peter Luschny_, Nov 22 2018