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, 6, 87, 2056, 71145, 3355956, 203899087, 15451934016, 1419181414929, 154796303577700, 19713331210664751, 2891162097251141616, 482733064744447450297, 90871916094948544512516, 19125402877558442317308975, 4467829768503489097383022336, 1151133088512781095709101702177, 325279313240363190497696752254276

Offset: 0

Author

David Einstein, Oct 09 2016

Keywords

• nonn

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).

Examples

			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]
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..272

Crossrefs

Cf. A181162, A239749-A239785, A239836-A239841.

Programs

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 *)

PARI

a(n) = sum(k = 1, n, n! / (n - k)! * binomial(n, k) * k^(2 * (n - k) ) ); \\ Joerg Arndt, Oct 10 2016

Formula

a(n) = Sum_{k=0..n} ((n! / (n - k)!) * C(n, k) * k^(2 * (n - k))).

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 20 2016