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

0, 1, 10, 114, 1556, 25080, 468462, 9971920, 238551336, 6339784320, 185391061010, 5917263922944, 204735466350780, 7633925334590464, 305188474579874550, 13023103577435351040, 590850477768105474128, 28401410966866912051200, 1441935117039649859464986

Offset: 0

Author

Geoffrey Critzer, Feb 09 2012

Keywords

• nonn

Comments

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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A000312, A001865, A076728, A185390.

Programs

Mathematica

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&];
  D[Range[0,nn]! CoefficientList[Series[Exp[tx]/(1-txy),{x,0,nn}],x],y]/.y->1

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

Formula

a(n) = (n+1)^(n+1) - A001865(n+1). - Seiichi Manyama, Jun 01 2019