cp's OEIS Frontend

A239761 Number of pairs of functions (f, g) on a set of n elements into itself satisfying f(g(x)) = f(x).

%I A239761 #36 Nov 16 2017 17:18:38
%S A239761 1,1,10,159,3496,98345,3373056,136535455,6371523712,336784920849,
%T A239761 19888195110400,1297716672601151,92721494240225280,
%U A239761 7199830049013964921,603715489091812335616,54366622743565012989375,5233114241479255004839936,536180296483497244155041825
%N A239761 Number of pairs of functions (f, g) on a set of n elements into itself satisfying f(g(x)) = f(x).
%H A239761 Alois P. Heinz, <a href="/A239761/b239761.txt">Table of n, a(n) for n = 0..345</a>
%F A239761 a(n) ~ 5^(-1/4) * ((1+sqrt(5))/2)^(3*n-1/2) * n^n / exp(2*n/(1+sqrt(5))). - _Vaclav Kotesovec_, Aug 07 2014
%F A239761 a(n) = Sum_{k = 1..n} A060281(n,k) n^k. - _David Einstein_, Oct 31 2016
%F A239761 a(n) = n! * [x^n] 1/(1 + LambertW(-x))^n. - _Ilya Gutkovskiy_, Oct 03 2017
%p A239761 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A239761       add(b(n-j, i-1)*binomial(n, j)*j^j, j=0..n)))
%p A239761     end:
%p A239761 a:= n-> b(n$2):
%p A239761 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 17 2014
%t A239761 f4[n_] := Sum[n^k Sum[Binomial[n - 1, j]*n^(n - 1 - j)*StirlingS1[j + 1, k] *(-1)^(j + k + 1), {j, 0, n - 1}], {k, 1, n}] (* _David Einstein_, Oct 31 2016 *)
%Y A239761 Cf. A181162, A239769, A239773.
%Y A239761 Column k=1 of A245910.
%Y A239761 Cf. A001622, A295188.
%K A239761 nonn
%O A239761 0,3
%A A239761 _Chad Brewbaker_, Mar 26 2014
%E A239761 a(6)-a(7) from _Giovanni Resta_, Mar 28 2014
%E A239761 a(8)-a(17) from _Alois P. Heinz_, Jul 17 2014