|
|
A247859
|
|
The product of the first n Catalan numbers and 2^(n^2).
|
|
0
|
|
|
1, 2, 32, 5120, 9175040, 197300060160, 53337309063413760, 187446932178571288903680, 8783433335287216312557974323200, 5597436690584888372318289416604667084800, 49290698636690081763273206158480893991348233830400, 6076713947745931800683801366458443411856602743866957548748800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The volume of a certain polytope (the type D_(n+2) Chan-Robbins-Yuen polytope). This was conjectured by Meszaros-Morales and proved independently by Zeilberger and Kim, both using a variant of the Morris constant term identity (just as for the original Chan-Robbins-Yuen polytope).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^(n^2) * prod(k=0..n) A000108(k).
|
|
MAPLE
|
seq(2^(n^2)*mul(binomial(2*k, k)/(1+k), k=0..n), n=0..13);
|
|
MATHEMATICA
|
a[n_] := 2^(n^2)*Product[ CatalanNumber[k], {k, 0, n}]; Table[a[n], {n, 0, 13}]
|
|
CROSSREFS
|
Cf. A003046 (Product of first n Catalan numbers).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|