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%I #12 Apr 03 2022 01:31:39
%S 1,1,1,1,2,1,1,4,4,1,1,8,11,8,1,1,16,28,28,16,1,1,32,71,87,71,32,1,1,
%T 64,184,266,266,184,64,1,1,128,491,823,952,823,491,128,1,1,256,1348,
%U 2598,3381,381,2598,1348,2561
%N Triangle generated from an array: A008277 * A008277(transform).
%C Row sums = A000995 such that row 1 = A000995(3) = 1.
%C This array is the product of the lower triangular Stirling matrix and its transpose, which explains why the array is symmetric. - _David Callan_, Dec 02 2011
%C In the triangle, T(n,k) is the number of permutations of [n+1] that avoid both dashed patterns 1-23 and 3-12, start with an ascent, and have first entry k. For example, T(4,2)=4 counts 23154, 24153, 24315, 25431. - _David Callan_, Dec 02 2011
%F Triangle read by rows = antidiagonals of an array formed by A008277 * A008277(transform), where A008277 = the Stirling number of the second kind triangle.
%e First few rows of the array:
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 4, 8, 16, 32, ...
%e 1, 4, 11, 28, 71, 184, ...
%e 1, 8, 28, 87, 266, 823, ...
%e 1, 16, 71, 266, 952, 3381, ...
%e ...
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 4, 4, 1;
%e 1, 8, 11, 8, 1;
%e 1, 16, 28, 28, 16, 1;
%e 1, 32, 71, 87, 71, 32, 1;
%e 1, 64, 184, 266, 266, 184, 64, 1;
%e 1, 128, 491, 823, 952, 823, 491, 128, 1;
%e ...
%Y Cf. A000995, A008277.
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, Feb 15 2008
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