cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A247859 The product of the first n Catalan numbers and 2^(n^2).

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%I A247859 #24 Sep 29 2014 19:11:21
%S A247859 1,2,32,5120,9175040,197300060160,53337309063413760,
%T A247859 187446932178571288903680,8783433335287216312557974323200,
%U A247859 5597436690584888372318289416604667084800,49290698636690081763273206158480893991348233830400,6076713947745931800683801366458443411856602743866957548748800
%N A247859 The product of the first n Catalan numbers and 2^(n^2).
%C A247859 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).
%H A247859 J. S. Kim, <a href="http://arxiv.org/abs/1407.3467">Proof of a conjecture of Mészáros and Morales on the volume of a flow polytope</a>, arXiv:1407.3467, 2014.
%H A247859 K. Mészáros, A. H. Morales, <a href="http://arxiv.org/abs/1208.0140">Flow polytopes of signed graphs and the Kostant partition function</a>, ArXiv:1208.0140, 2012.
%H A247859 D. Zeilberger, <a href="http://arxiv.org/abs/1407.2829">Sketch of a Proof of an Intriguing Conjecture of Karola Mészáros and Alejandro Morales Regarding the Volume of the Dn Analog of the Chan-Robbins-Yuen Polytope (Or: The Morris-Selberg Constant Term Identity Strikes Again!)</a>, arXiv:1407.2829, 2014.
%F A247859 a(n) = 2^(n^2) * A003046(n).
%F A247859 a(n) = 2^(n^2) * prod(k=0..n) A000108(k).
%p A247859 seq(2^(n^2)*mul(binomial(2*k, k)/(1+k), k=0..n), n=0..13);
%t A247859 a[n_] := 2^(n^2)*Product[ CatalanNumber[k], {k, 0, n}]; Table[a[n], {n, 0, 13}]
%Y A247859 Cf. A000108 (Catalan numbers).
%Y A247859 Cf. A003046 (Product of first n Catalan numbers).
%K A247859 nonn,easy
%O A247859 0,2
%A A247859 _Alejandro H. Morales_, Sep 25 2014