This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A277337 #12 Nov 02 2016 11:38:38 %S A277337 1,1,6,87,2056,71145,3355956,203899087,15451934016,1419181414929, %T A277337 154796303577700,19713331210664751,2891162097251141616, %U A277337 482733064744447450297,90871916094948544512516,19125402877558442317308975,4467829768503489097383022336,1151133088512781095709101702177,325279313240363190497696752254276 %N A277337 Number of pairs of functions (f,g) from a set of n elements into itself that are generalized reflexive inverses of each other. %C A277337 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 A277337 Alois P. Heinz, <a href="/A277337/b277337.txt">Table of n, a(n) for n = 0..272</a> %F A277337 a(n) = Sum_{k=0..n} ((n! / (n - k)!) * C(n, k) * k^(2 * (n - k))). %e A277337 For n=2 the a(2)=6 solutions are %e A277337 1: [1,1] [1,1] %e A277337 2: [1,1] [2,2] %e A277337 3: [2,2] [1,1] %e A277337 4: [2,2] [2,2] %e A277337 5: [1,2] [1,2] %e A277337 6: [2,1] [2,1] %t A277337 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 A277337 (PARI) a(n) = sum(k = 1, n, n! / (n - k)! * binomial(n, k) * k^(2 * (n - k) ) ); \\ _Joerg Arndt_, Oct 10 2016 %Y A277337 Cf. A181162, A239749-A239785, A239836-A239841. %K A277337 nonn %O A277337 0,3 %A A277337 _David Einstein_, Oct 09 2016 %E A277337 a(0)=1 prepended by _Alois P. Heinz_, Oct 20 2016