|
|
A189769
|
|
Number of one-sided prudent walks from (0,0) to (n,n), with 3+n east steps, 3 west steps and n north steps.
|
|
1
|
|
|
2, 24, 200, 1400, 8820, 51744, 288288, 1544400, 8022300, 40646320, 201753552, 984312784, 4732273000, 22465296000, 105479913600, 490481598240, 2261264427180, 10345654242000, 47009200854000, 212283654382800, 953254695633240, 4258696302569280, 18936890673480000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n+1)*(2+n)*Gamma(2*n)/(3*(Gamma(n)^2).
|
|
MATHEMATICA
|
Table[(n+1)*(2+n) Gamma[2*n]/(3 (Gamma[n])^2), {n, 30}] (* T. D. Noe, Apr 29 2011 *)
|
|
PROG
|
(Magma) [ Round((n+1)*(n+2)*Gamma(2*n)/(3*Gamma(n)^2)): n in [1..23] ]; // Klaus Brockhaus, Apr 29 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|