A277337 - OEIS

%I #12 Nov 02 2016 11:38:38

%S 1,1,6,87,2056,71145,3355956,203899087,15451934016,1419181414929,

%T 154796303577700,19713331210664751,2891162097251141616,

%U 482733064744447450297,90871916094948544512516,19125402877558442317308975,4467829768503489097383022336,1151133088512781095709101702177,325279313240363190497696752254276

%N Number of pairs of functions (f,g) from a set of n elements into itself that are generalized reflexive inverses of each other.

%C 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).

%H Alois P. Heinz, <a href="/A277337/b277337.txt">Table of n, a(n) for n = 0..272</a>

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

%e For n=2 the a(2)=6 solutions are

%e 1: [1,1] [1,1]

%e 2: [1,1] [2,2]

%e 3: [2,2] [1,1]

%e 4: [2,2] [2,2]

%e 5: [1,2] [1,2]

%e 6: [2,1] [2,1]

%t 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 *)

%o (PARI) a(n) = sum(k = 1, n, n! / (n - k)! * binomial(n, k) * k^(2 * (n - k) ) ); \\ _Joerg Arndt_, Oct 10 2016

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

%K nonn

%O 0,3

%A _David Einstein_, Oct 09 2016

%E a(0)=1 prepended by _Alois P. Heinz_, Oct 20 2016