|
| |
|
|
A109984
|
|
Number of steps in all Delannoy paths of length n (a Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1) and D=(1,1)).
|
|
1
| |
|
|
0, 5, 44, 321, 2184, 14325, 91860, 580097, 3622928, 22437477, 138049020, 844881345, 5148375192, 31258302933, 189199514532, 1142148091905, 6878977097760, 41347348295877, 248082231062988, 1486116788646977
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(n)=sum(k*A109983(k),k=0..2n).
|
|
|
REFERENCES
| R. A. Sulanke, Objects counted by the central Delannoy numbers, J. of Integer Sequences, 6, 2003, Article 03.1.5.
|
|
|
FORMULA
| a(n)=sum(k*binomial(n, 2n-k)*binomial(k, n), k=n..2n). G.f.=z*(5-z)/(1-6z+z^2)^(3/2).
|
|
|
EXAMPLE
| a(1)=5 because in the 3 (=A001850(1)) Delannoy paths of length 1, namely D,NE and EN, we have alltogether five steps.
|
|
|
MAPLE
| a:=n->add(k*binomial(n, 2*n-k)*binomial(k, n), k=n..2*n): seq(a(n), n=0..23);
|
|
|
CROSSREFS
| Cf. A109983, A001850.
Sequence in context: A173376 A128523 A068311 * A096355 A054766 A195242
Adjacent sequences: A109981 A109982 A109983 * A109985 A109986 A109987
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 07 2005
|
| |
|
|
