OFFSET
3,3
COMMENTS
The asymptotic value for large n is 0.051615...*n! = (e - 8/3)*n!. See also comment for A079884.
REFERENCES
See under A079884.
LINKS
FORMULA
a(3)=0, a(n) = n * a(n-1) + 1 for n >= 4.
For n >= 3, a(n) = floor(c*n!) where c = lim_{n->infinity} a(n)/n! = 0.05161516179237856869. - Benoit Cloitre
a(n) = Sum_{j=4..n} (n-j)! * binomial(n,j). - Zerinvary Lajos, Jul 31 2006
E.g.f.: (exp(x) - Sum_{k=0..3} x^k/k!) / (1 - x). - Ilya Gutkovskiy, Jun 26 2022
MAPLE
a:=n->sum((n-j)!*binomial(n, j), j=4..n): seq(a(n), n=3..25); # Zerinvary Lajos, Jul 31 2006
MATHEMATICA
a[3] = 0; a[n_] := n*a[n - 1] + 1; Table[a[n], {n, 3, 21}]
PROG
FORTRAN program available at link
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Hugo Pfoertner, Jan 14 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jan 22 2003
STATUS
approved