A183264 Number of singly defective permutations of 1..n with exactly 1 maximum.

0, 2, 15, 64, 220, 672, 1904, 5120, 13248, 33280, 81664, 196608, 465920, 1089536, 2519040, 5767168, 13090816, 29491200, 65994752, 146800640, 324796416, 715128832, 1567621120, 3422552064, 7444889600, 16139681792, 34879832064, 75161927680, 161531035648, 346281738240

Offset

1,2

Comments

A singly defective permutation omits one value and repeats another value.

a(1) is zero because there are no defective permutations of a single element.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Formula

Conjecture: a(n) = n * (3*n-4) * 2^(n-3) for n > 1. - Andrew Howroyd, May 12 2020

Example

Some solutions for n=3 with 1 maximum:
(3,3,2) (1,3,3) (1,1,2) (2,1,1) (3,3,1) (1,3,1) (1,2,2) (2,2,1) (2,2,3).

Crossrefs

Column 1 of A183270.

Cf. A053220.

Sequence in context: A267596 A119904 A271828 * A176972 A117393 A055206

Adjacent sequences: A183261 A183262 A183263 * A183265 A183266 A183267

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Extensions

Terms a(16) and beyond from Andrew Howroyd, May 12 2020

Status

approved