login
A277337
Number of pairs of functions (f,g) from a set of n elements into itself that are generalized reflexive inverses of each other.
1
1, 1, 6, 87, 2056, 71145, 3355956, 203899087, 15451934016, 1419181414929, 154796303577700, 19713331210664751, 2891162097251141616, 482733064744447450297, 90871916094948544512516, 19125402877558442317308975, 4467829768503489097383022336, 1151133088512781095709101702177, 325279313240363190497696752254276
OFFSET
0,3
COMMENTS
The number of pairs of functions (f,g) from a set of n elements into itself such that f(g(f(x))) = f(x) and g(f(g(x))) = g(x).
LINKS
FORMULA
a(n) = Sum_{k=0..n} ((n! / (n - k)!) * C(n, k) * k^(2 * (n - k))).
EXAMPLE
For n=2 the a(2)=6 solutions are
1: [1,1] [1,1]
2: [1,1] [2,2]
3: [2,2] [1,1]
4: [2,2] [2,2]
5: [1,2] [1,2]
6: [2,1] [2,1]
MATHEMATICA
Flatten[{1, Table[Sum[n!*Binomial[n, k]*k^(2*(n-k))/(n-k)!, {k, 1, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 21 2016 *)
PROG
(PARI) a(n) = sum(k = 1, n, n! / (n - k)! * binomial(n, k) * k^(2 * (n - k) ) ); \\ Joerg Arndt, Oct 10 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
David Einstein, Oct 09 2016
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 20 2016
STATUS
approved