OFFSET
1,2
COMMENTS
A122852 is another version of the same sequence. - R. J. Mathar, Jun 18 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
FORMULA
The sequence 1, 1, 2, 3, .. has a(n)=sum{k=0..floor(n/2), C(n-k, k)k!} (diagonal sums of permutation triangle A008279). - Paul Barry, May 12 2004
Recurrence: 2*a(n) = 3*a(n-1) + (n-1)*a(n-2) - (n-1)*a(n-3). - Vaclav Kotesovec, Feb 08 2014
a(n) ~ sqrt(Pi) * exp(sqrt(n/2) - n/2 + 1/8) * n^((n+1)/2) / 2^(n/2+1) * (1 + 37/(48*sqrt(2*n))). - Vaclav Kotesovec, Feb 08 2014
MATHEMATICA
Table[Sum[Binomial[n-k, k]*k!, {k, 0, Floor[n/2]}], {n, 1, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 19 2002
STATUS
approved