A183270 T(n,k) is the number of singly defective permutations of 1..n+2*k-2 with exactly k maxima.

0, 3, 2, 120, 80, 15, 4760, 3552, 860, 64, 249984, 199168, 57064, 6576, 220, 17512704, 14548480, 4643712, 681984, 42112, 672, 1599330304, 1367568384, 469942528, 80506880, 6849792, 242688, 1904, 185616337920, 162107703296, 58754129408

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn
• tabl

Comments

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

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

T(n,k) is divisible by n + 2*k - 2. - Andrew Howroyd, May 12 2020

Examples

			Table starts:
     0      3     120     4760    249984   17512704 1599330304 ...
     2     80    3552   199168  14548480 1367568384 ...
    15    860   57064  4643712 469942528 ...
    64   6576  681984 80506880 ...
   220  42112 6849792 ...
   672 242688 ...
  1904 ...
  ...
Some solutions for n=4 with 2 maxima:
(6,1,4,4,3,2) (4,3,1,5,6,6) (4,2,1,2,3,5) (3,2,1,6,4,3) (5,5,6,1,2,3).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (terms 1..36 from R. H. Hardin)

Crossrefs

Columns 1..6 are A183264, A183265, A183266, A183267, A183268, A183269.

Cf. A001804, A008303, A334774.

Programs

PARI

\\ PeaksBySig defined in A334774.
T(n,k) = {my(m=n+2*k-3); (m+1)*sum(i=1, m, PeaksBySig(vector(m,j,if(i==j,2,1)), [k-1])[1])} \\ Andrew Howroyd, May 12 2020

Formula

A001804(n) = Sum_{k=1..2*n+1} T(n+2-2*k, k). - Andrew Howroyd, May 12 2020