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A185391 a(n) = Sum_{k=0..n} A185390(n,k) * k.

%I A185391 #40 Jun 01 2019 09:34:57
%S A185391 0,1,10,114,1556,25080,468462,9971920,238551336,6339784320,
%T A185391 185391061010,5917263922944,204735466350780,7633925334590464,
%U A185391 305188474579874550,13023103577435351040,590850477768105474128,28401410966866912051200,1441935117039649859464986
%N A185391 a(n) = Sum_{k=0..n} A185390(n,k) * k.
%C A185391 The total number of elements, x in the domain of definition of all partial functions on n labeled objects such that for all i in {1,2,3,...} (f^i)(x) is defined.
%H A185391 G. C. Greubel, <a href="/A185391/b185391.txt">Table of n, a(n) for n = 0..385</a>
%F A185391 a(n) = (n+1)^(n+1) - A001865(n+1). - _Seiichi Manyama_, Jun 01 2019
%t A185391 nn=20; tx=Sum[n^(n-1) x^n/n!,{n,1,nn}]; txy=Sum[n^(n-1) (x y)^n/n!, {n,1,nn}]; f[list_] := Select[list, #>0&];
%t A185391   D[Range[0,nn]! CoefficientList[Series[Exp[tx]/(1-txy),{x,0,nn}],x],y]/.y->1
%o A185391 (PARI) {a(n) = (n+1)^(n+1)-sum(k=1, n+1, binomial(n+1, k)*k^k*(n+1-k)^(n+1-k))/(n+1)} \\ _Seiichi Manyama_, Jun 01 2019
%Y A185391 Cf. A000312, A001865, A076728, A185390.
%K A185391 nonn
%O A185391 0,3
%A A185391 _Geoffrey Critzer_, Feb 09 2012