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).

1, 1, 2, 2, 5, 6, 6, 18, 25, 26, 24, 84, 134, 149, 150, 120, 480, 870, 1050, 1081, 1082, 720, 3240, 6600, 8700, 9302, 9365, 9366, 5040, 25200, 57120, 82320, 92526, 94458, 94585, 94586, 40320, 221760, 554400, 871920, 1038744, 1085364, 1091414

Offset

1,3

Comments

Can be generated from Stirling_2 triangle A008277 (cf. A028246, which is intermediate between the two arrays).

Links

Table of n, a(n) for n=1..43.

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.

Example

1;
1,  2;
2,  5,  6;
6, 18, 25, 26; ...

Crossrefs

Row sums give A000670. First 3 rows are A000629, A002050 = A000629 - 1, 2*A002051 = (A000629 - 2^m) (m >= 0)

Sequence in context: A209744 A209465 A209527 * A063177 A249521 A355345

Adjacent sequences: A054252 A054253 A054254 * A054256 A054257 A054258

Keyword

nonn,tabl

Author

Eugene McDonnell (Eemcd(AT)aol.com), May 05 2000

Extensions

More terms from James A. Sellers, May 05 2000

Status

approved