

A185391


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


1



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

0,3


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


FORMULA

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


MATHEMATICA

nn=20; tx=Sum[n^(n1) x^n/n!, {n, 1, nn}]; txy=Sum[n^(n1) (x y)^n/n!, {n, 1, nn}]; f[list_] := Select[list, #>0&];
D[Range[0, nn]! CoefficientList[Series[Exp[tx]/(1txy), {x, 0, nn}], x], y]/.y>1


PROG

(PARI) {a(n) = (n+1)^(n+1)sum(k=1, n+1, binomial(n+1, k)*k^k*(n+1k)^(n+1k))/(n+1)} \\ Seiichi Manyama, Jun 01 2019


CROSSREFS

Cf. A000312, A001865, A076728, A185390.
Sequence in context: A176824 A196983 A199908 * A104520 A138845 A079678
Adjacent sequences: A185388 A185389 A185390 * A185392 A185393 A185394


KEYWORD

nonn


AUTHOR

Geoffrey Critzer, Feb 09 2012


STATUS

approved



