|
Search: id:A052568
|
|
|
| A052568 |
|
A simple regular expression in a labeled universe. |
|
+0
1
|
|
| 1, 2, 10, 78, 816, 10680, 167760, 3074400, 64391040, 1517201280, 39720844800, 1143895737600, 35937095040000, 1223098971494400, 44829605505484800, 1760481463732992000, 73744004937867264000, 3282093293695856640000
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Laguerre transform of n!F(n+1)=A005442 [From Paul Barry (pbarry(AT)wit.ie), Aug 08 2008]
|
|
LINKS
|
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 510
|
|
FORMULA
|
E.g.f.: -(-1+x)/(1-3*x+x^2)
Recurrence: {a(0)=1, a(1)=2, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)}
Sum(1/5*(1+_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!
a(n)=sum{k=0..n, binomial(n,k)(n!/k!)*k!F(k+1)}. [From Paul Barry (pbarry(AT)wit.ie), Aug 08 2008]
|
|
MAPLE
|
spec := [S, {S=Sequence(Union(Z, Prod(Z, Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
CROSSREFS
|
Adjacent sequences: A052565 A052566 A052567 this_sequence A052569 A052570 A052571
Sequence in context: A134980 A098692 A138273 this_sequence A063170 A098636 A081363
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
|
Search completed in 0.002 seconds
|
