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A183270
T(n,k) is the number of singly defective permutations of 1..n+2*k-2 with exactly k maxima.
7
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
1,2
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
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (terms 1..36 from R. H. Hardin)
FORMULA
A001804(n) = Sum_{k=1..2*n+1} T(n+2-2*k, k). - Andrew Howroyd, May 12 2020
EXAMPLE
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).
PROG
(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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 03 2011
STATUS
approved