A108694 Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 2, 2, 4, 3, 6, 4, 8, 5, 10, 6, 12, . . . ] DELTA [2, 1, 4, 2, 6, 3, 8, 4, 10, 5, 12, 6, . . . ] where DELTA is the operator defined in A084938.

1, 1, 2, 3, 9, 6, 13, 54, 69, 26, 75, 399, 747, 573, 150, 541, 3508, 8638, 9998, 5393, 1082, 4683, 35817, 109248, 169038, 139143, 57585, 9366, 47293, 416762, 1515531, 2935222, 3256907, 2064534, 691645, 94586

Offset: 0

Author

Philippe Deléham, Jun 18 2005

Keywords

• easy
• nonn
• tabl

Comments

Related to preferential arrangements of n elements (A000670) and necklaces of sets of labeled beads (A000629).

Examples

			1; 1, 2; 3, 9, 6; 13, 54, 69, 26; 75, 399, 747, 573, 150; ...
		

Crossrefs

Cf. A000629, A000670, A032031, A084938.

Formula

Sum_{ k>=0 } T(n, k) = n!*3^n = A032031(n).

T(n, 0) = A000670(n); T(n, n) = A000629(n).