A091441 Table (by antidiagonals) of permutations of two types of objects such that each cycle contains at least one object of each type. Each type of object is labeled from its own label set.

1, 2, 2, 6, 8, 6, 24, 36, 36, 24, 120, 192, 216, 192, 120, 720, 1200, 1440, 1440, 1200, 720, 5040, 8640, 10800, 11520, 10800, 8640, 5040, 40320, 70560, 90720, 100800, 100800, 90720, 70560, 40320, 362880, 645120, 846720, 967680, 1008000, 967680

Offset

1,2

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 114 (2.4.42).

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Formula

Double e.g.f.: A(x, y) = Sum_{i, j>=0} (x^i*y^j/(i!*j!)) = (1-x)*(1-y)/(1-x-y).

T(n,k) = k * T(n-1,k-1) + (n-k+1) * T(n-1,k), T(1,1) = 1. - Reinhard Zumkeller, May 07 2013

Example

    1,    2,     6,     24,     120; ...
    2,    8,    36,    192,    1200; ...
    6,   36,   216,   1440,   10800; ...
   24,  192,  1440,  11520,  100800; ...
  120, 1200, 10800, 100800, 1008000; ...

Prog

(Haskell)
import Data.List (genericLength)
a091441 n k = a091441_tabl !! (n-1) !! (k-1)
a091441_row n = a091441_tabl !! (n-1)
a091441_tabl = iterate f [1] where
   f xs = zipWith (+)
     (zipWith (*) ([0] ++ xs) ks) (zipWith (*) (xs ++ [0]) (reverse ks))
     where ks = [1 .. 1 + genericLength xs]
-- Reinhard Zumkeller, May 07 2013

Crossrefs

Cf. A008292.

Sequence in context: A231131 A142243 A269722 * A269565 A334518 A099490

Adjacent sequences: A091438 A091439 A091440 * A091442 A091443 A091444

Keyword

nonn,tabl

Author

Christian G. Bower, Jan 09 2004

Status

approved