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A054255 Triangle T(n,k) (n >= 1, 0<=k<=n) giving number of preferential arrangements of n things beginning with k (transposed, then read by rows).

%I A054255 #16 Jul 02 2025 16:01:59
%S A054255 1,1,2,2,5,6,6,18,25,26,24,84,134,149,150,120,480,870,1050,1081,1082,
%T A054255 720,3240,6600,8700,9302,9365,9366,5040,25200,57120,82320,92526,94458,
%U A054255 94585,94586,40320,221760,554400,871920,1038744,1085364,1091414,1091669,1091670
%N A054255 Triangle T(n,k) (n >= 1, 0<=k<=n) giving number of preferential arrangements of n things beginning with k (transposed, then read by rows).
%C A054255 Can be generated from Stirling_2 triangle A008277 (cf. A028246, which is intermediate between the two arrays).
%H A054255 N. J. A. Sloane and Thomas Wieder, <a href="http://arXiv.org/abs/math.CO/0307064">The Number of Hierarchical Orderings</a>, Order 21 (2004), 83-89.
%e A054255    1;
%e A054255    1,  2;
%e A054255    2,  5,   6;
%e A054255    6, 18,  25,  26;
%e A054255   24, 84, 134, 149, 150;
%e A054255   ...
%Y A054255 Row sums give A000670. First 3 rows are A000629, A002050 = A000629 - 1, 2*A002051 = (A000629 - 2^m) (m >= 0).
%Y A054255 Cf. A090665 (triangle with rows reversed).
%K A054255 nonn,tabl
%O A054255 1,3
%A A054255 Eugene McDonnell (Eemcd(AT)aol.com), May 05 2000
%E A054255 More terms from _James Sellers_, May 05 2000