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^(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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Feb 09 2012
STATUS
approved