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

Author

Alejandro H. Morales, Oct 04 2014

Keywords

• nonn
• easy

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

Links

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

Crossrefs

Cf. A000108, A003046, A005118, A008608.

Programs

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;

Formula

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

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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