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

0,3

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

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

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

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

Sequence in context: A365011 A123544 A239749 * A138216 A294491 A239750

Adjacent sequences: A277334 A277335 A277336 * A277338 A277339 A277340

Keyword

nonn

Author

David Einstein, Oct 09 2016

Extensions

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

Status

approved