

A273935


Number of ways to arrange n women and n men around a circular table so that they can be divided into n nonintersecting pairs of 1 woman and 1 man sitting sidebyside.


0



1, 1, 6, 84, 2160, 89280, 5443200, 460857600, 51819264000, 7476605337600, 1347105779712000, 296508121620480000, 78297264318873600000, 24431729220414996480000, 8893692297263669575680000, 3735464765667589501747200000, 1793050447716486548029440000000
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OFFSET

0,3


COMMENTS

a(n) is the number of monotonic paths from (0,0) to (n,n) which are equivalent to a path which is no more than 1 step from the main diagonal, where two paths are equivalent if they are circular shifts of one another.


LINKS

Table of n, a(n) for n=0..16.


FORMULA

a(n) = n!*(n1)!*(2^n1) for n>0, a(0) = 1.
a(n) = A000142(n)*A000142(n1)*A000225(n), n >= 1.  Omar E. Pol, Jun 16 2016


EXAMPLE

For n = 2: Represent the women and men as the numbers 1,2,3,4, where 1,3 are women and 2,4 are men. Then all 6 arrangements around the circular table are valid (parentheses included to emphasize a valid pairing, including wraparound):
(1,2),(3,4);
(1,2),(4,3);
1),(3,2),(4;
1),(3,4),(2;
(1,4),(2,3);
(1,4),(3,2).


PROG

(PARI) a(n) = if (n==0, 1, n!*(n1)!*(2^n1)); \\ Michel Marcus, Jun 20 2016


CROSSREFS

Cf. A000142, A000225, A010790.
Sequence in context: A010794 A177560 A177562 * A318399 A171200 A195245
Adjacent sequences: A273932 A273933 A273934 * A273936 A273937 A273938


KEYWORD

nonn


AUTHOR

Vincent Chan, Jun 16 2016


STATUS

approved



