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A112858 Table read by antidiagonals: T(n,k) = count of increasing runs in strings of length n*k formed by concatenating k permutations of [n]. 2
1, 2, 3, 3, 11, 12, 4, 32, 132, 60, 5, 84, 1152, 2664, 360, 6, 208, 9072, 93312, 80640, 2520, 7, 496, 67392, 2944512, 14169600, 3412800, 20160, 8, 1152, 482112, 87588864, 2239488000, 3608064000, 192326400, 181440, 9, 2624, 3359232, 2508226560 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The first column T(n,1) is A001710(n+1), i.e., (n+1)!/2. The 2nd column T(n,2) is the outer diagonal of triangle A122823.

LINKS

Table of n, a(n) for n=1..40.

FORMULA

T(n,k) = (k(n+1)/2 - (k-1)(n-1)/2n) * (n!)^k.

EXAMPLE

Table begins:

   1    2     3       4 ...

   3   11    32      84 ...

  12  132  1152    9072 ...

  60 2664 93312 2944512 ...

  ...

Example: Take the permutations of [2], namely, 12 and 21, and form all possible strings that are concatenations of 2 of these permutations. These are 1212, 1221, 2112, 2121 with 2, 3, 3, 3 increasing runs respectively. T(2,2) = 2 + 3 + 3 + 3 = 11.

CROSSREFS

Cf. A001710, A110952, A122823.

Sequence in context: A210755 A219224 A265532 * A161960 A287428 A232933

Adjacent sequences:  A112855 A112856 A112857 * A112859 A112860 A112861

KEYWORD

easy,nonn,tabl

AUTHOR

David Scambler, Nov 22 2006

STATUS

approved

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Last modified July 19 08:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)