A248330 The product of the first n Catalan numbers and the number of standard Young tableaux of shape(1,2,...,n).

1, 1, 4, 160, 107520, 1722040320, 854352419880960, 16185399027773630054400, 13931397052191274338996977664000, 632089112919018408339999461491467091968000, 1721041721929360607907210006858724622834371563356160000

Offset

0,3

Comments

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).

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).

Links

Table of n, a(n) for n=0..10.

K. Mészáros, A.H. Morales, B. Rhoades, The polytope of Tesler matrices, ArXiv:1409.8566, 2014.

Formula

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

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

Maple

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;

Crossrefs

Cf. A000108, A003046, A005118, A008608.

Sequence in context: A224198 A104133 A214007 * A157463 A041779 A222394

Adjacent sequences: A248327 A248328 A248329 * A248331 A248332 A248333

Keyword

nonn,easy

Author

Alejandro H. Morales, Oct 04 2014

Status

approved