A092741 Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding both the 132- and the 321-pattern is equal to k.

1, 0, 2, 0, 2, 4, 0, 8, 9, 7, 0, 40, 45, 24, 11, 0, 240, 270, 144, 50, 16, 0, 1680, 1890, 1008, 350, 90, 22, 0, 13440, 15120, 8064, 2800, 720, 147, 29, 0, 120960, 136080, 72576, 25200, 6480, 1323, 224, 37, 0, 1209600, 1360800, 725760, 252000, 64800, 13230

Offset: 1

Author

Emeric Deutsch, Apr 12 2004

Keywords

• nonn
• tabl

Comments

Row sums are the factorial numbers (A000142).

T(n,2)=n!/3 for n>=3 (A002301). T(n,3)=3n!/8 for n>=4.

Diagonal yields A000124.

Examples

			T(3,2)=2 because only 132 and 321 satisfy the requirements.
		

Links

• E. Deutsch and W. P. Johnson, Create your own permutation statistics, Math. Mag., 77, 130-134, 2004.
• R. Simion and F. W. Schmidt, Restricted permutations, European J. Combin., 6, 383-406, 1985.

Crossrefs

Cf. A000142, A002301, A000124.

Formula

T(n, k) = n!k/[2(k-2)!(k+1)] for k

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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