OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..424
H. Belbachir, Y. Djemmada and L. Németh, The deranged Bell numbers, arXiv:2102.00139 [math.GM], 2021.
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k)*A000166(k).
E.g.f.: exp(-(exp(x)-1))/(2-exp(x)).
a(n) ~ n!/(2*exp(1)*log(2)^(n+1)). - Vaclav Kotesovec, Jun 29 2013
MAPLE
g:= proc(n) option remember;
`if`(n<2, 1-n, (n-1)*(g(n-1)+g(n-2)))
end:
b:= proc(n, m) option remember;
`if`(n=0, g(m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..27); # Alois P. Heinz, Feb 16 2023
MATHEMATICA
A000166[n_] := Round[ n!/Exp[1] ]; A000166[0] = 1; A000166[1] = 0; a[n_] := Sum[ StirlingS2[n, k]*A000166[k], {k, 0, n}]; Table[ a[n], {n, 0, 18}] (* Jean-François Alcover, Dec 21 2011, after given formula *)
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Karol A. Penson, Oct 12 2001
STATUS
approved