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A333726 Triangle read by rows: T(n,k) is the number of permutations in S_n for which all cycles are length k or greater. 2
1, 2, 1, 6, 2, 2, 24, 9, 6, 6, 120, 44, 24, 24, 24, 720, 265, 160, 120, 120, 120, 5040, 1854, 1140, 720, 720, 720, 720, 40320, 14833, 8988, 6300, 5040, 5040, 5040, 5040, 362880, 133496, 80864, 58464, 40320, 40320, 40320, 40320, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Steven Finch, Second best, Third worst, Fourth in line, arxiv:2202.07621 [math.CO], 2022.

FORMULA

T(n,k) = 0 when n < k,

T(n,k) = (n-1)! when n = k, and otherwise

T(n,k) = (n-1) * T(n-1, k) + A068424(n-1, k-1) * T(n-k, k).

EXAMPLE

Triangle begins:

n\k|      1      2     3     4     5     6     7     8     9

---+--------------------------------------------------------

  1|      1

  2|      2      1

  3|      6      2     2

  4|     24      9     6     6

  5|    120     44    24    24    24

  6|    720    265   160   120   120   120

  7|   5040   1854  1140   720   720   720   720

  8|  40320  14833  8988  6300  5040  5040  5040  5040

  9| 362880 133496 80864 58464 40320 40320 40320 40320 40320

CROSSREFS

Columns 1-4: A000142, A000166, A038205, A047865.

Cf. A068424.

Sequence in context: A351442 A325815 A292441 * A306549 A198870 A050457

Adjacent sequences:  A333723 A333724 A333725 * A333727 A333728 A333729

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Apr 23 2020

STATUS

approved

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Last modified May 26 04:43 EDT 2022. Contains 354074 sequences. (Running on oeis4.)