OFFSET
0,4
FORMULA
G.f.: (2*x)/(-2*x^2*y+4*x+sqrt(1-4*x)-1).
T(n,m) = Sum_{k=1..n-m} k/(n-m) * C(2*n-2*m,n-m-k) * C(k+m,k).
EXAMPLE
1;
1, 1;
3, 2, 1;
10, 7, 3, 1;
126, 99, 49, 18, 5, 1;
Forests have 4 edges and 2 trees. T(3,1)=7.
|...........|.....x.x.|....x.x...|
|....x.x.x.x|....x.o..|.....o.x..|
|.r.....r...|.r...r...|.r....r...|
.................................
|.x.x..x.x.|
| .r....r..|
''''''''''''''''''''''''''''''''''
|...........|..x.x....|.x.x......|
|.x.x.x.x...|.x.o.....|..o.x.....|
|....r....r.|..r....r.|...r....r.|
PROG
(Maxima) T(n, m):=if n=m then 1 else sum(k/(n-m)*binomial(2*n-2*m, n-m-k)*binomial(k+m, k), k, 1, n-m);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Mar 28 2019
STATUS
approved