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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 side-by-side. 0
1, 1, 6, 84, 2160, 89280, 5443200, 460857600, 51819264000, 7476605337600, 1347105779712000, 296508121620480000, 78297264318873600000, 24431729220414996480000, 8893692297263669575680000, 3735464765667589501747200000, 1793050447716486548029440000000 (list; graph; refs; listen; history; text; internal format)
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!*(n-1)!*(2^n-1) for n>0, a(0) = 1.

a(n) = A000142(n)*A000142(n-1)*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!*(n-1)!*(2^n-1)); \\ 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

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)