|
| |
|
|
A111063
|
|
a(0) = 1; a(n) = (n-1)*a(n-1)+n.
|
|
0
| |
|
|
1, 1, 3, 9, 31, 129, 651, 3913, 27399, 219201, 1972819, 19728201, 217010223, 2604122689, 33853594971, 473950329609, 7109254944151, 113748079106433, 1933717344809379, 34806912206568841, 661331331924807999, 13226626638496160001, 277759159408419360043
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Contribution from Frank Ruskey (ruskey(AT)cs.uvic.ca), Nov 24 2009: (Start)
If the initial 1 were deleted, the recurrence relation becomes a(n) = n+1+n*a(n-1) with a(0) = 1. Furthermore, it can then be shown that a(n) is the number of non-empty subsets of binary strings with n 1's and 2 0's that are closed under the operation of replacing the leftmost 01 with 10. Taking the maximal elements under this relation,
a(2) = 9 = |{0011},{0101},{1001},{1010},{1100},{0110}, {0110,1001},{0101,0110},{0011,0110}|.
We also have the e.g.f. (1+x)/(1-x) e^x and the formula a(n) = -1 + 2 n! SUM( 1/j!, j=0..n ). (End)
|
|
|
FORMULA
| a(n+1)=sum{k=0..2n, C(n,floor(k/2))(n-floor(k/2))!}; - Paul Barry (pbarry(AT)wit.ie), May 04 2007
a(n)= 2*floor(e*n!)-1, n>1 [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 10 2010]
|
|
|
MAPLE
| a:=proc(n) option remember; if n=0 then RETURN(1); fi; (n-1)*a(n-1)+n; end;
|
|
|
MATHEMATICA
| a=2; lst={}; Do[a=n*2+a*(n-1); AppendTo[lst, a/2], {n, 0, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 16 2010]
|
|
|
CROSSREFS
| A030297(n)/n, n>0.
a(n) = A007526(n) + A000522(n) [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 10 2010]
Sequence in context: A071603 A090595 A027040 * A089475 A099999 A039749
Adjacent sequences: A111060 A111061 A111062 * A111064 A111065 A111066
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 08 2005
|
| |
|
|
