A248330 - OEIS

%I #13 Jul 05 2015 00:41:23

%S 1,1,4,160,107520,1722040320,854352419880960,16185399027773630054400,

%T 13931397052191274338996977664000,

%U 632089112919018408339999461491467091968000,1721041721929360607907210006858724622834371563356160000

%N The product of the first n Catalan numbers and the number of standard Young tableaux of shape(1,2,...,n).

%C The volume of a certain polytope (the Tesler polytope) whose lattice points are Tesler matrices (A008608), and with (n+1)! integral vertices (permutation Tesler matrices).

%C This is also the iterated constant term of the rational function (x1+x2+...+xn+x(n+1))^binomial(n+1,2)*product_{1<=i<j<=n+1}(xj-xi)^(-1).

%H K. Mészáros, A.H. Morales, B. Rhoades, <a href="http://arxiv.org/abs/1409.8566">The polytope of Tesler matrices</a>, ArXiv:1409.8566, 2014.

%F a(n) = A005118(n+1) * A003046(n).

%F a(n) = A005118(n+1) * Product_{k=0..n} A000108(k).

%p A248330 := proc(n) local i; mul(binomial(2*k, k)/(1+k), k=0..n)*binomial(n+1, 2)!/ mul( (2*i+1)^(n-i), i=0..n-1 ); end;

%Y Cf. A000108, A003046, A005118, A008608.

%K nonn,easy

%O 0,3

%A _Alejandro H. Morales_, Oct 04 2014