login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
K. Mészáros, A. H. Morales, Flow polytopes of signed graphs and the Kostant partition function, ArXiv:1208.0140, 2012.
FORMULA
a(n) = 2^(n^2) * A003046(n).
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. A000108 (Catalan numbers).
Cf. A003046 (Product of first n Catalan numbers).
Sequence in context: A053853 A018241 A012599 * A202629 A129349 A180127
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)