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 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 J. S. Kim, Proof of a conjecture of Mészáros and Morales on the volume of a flow polytope, arXiv:1407.3467, 2014. 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 Adjacent sequences:  A247856 A247857 A247858 * A247860 A247861 A247862 KEYWORD nonn,easy AUTHOR Alejandro H. Morales, Sep 25 2014 STATUS approved

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Last modified September 15 16:33 EDT 2019. Contains 327078 sequences. (Running on oeis4.)