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A248330 The product of the first n Catalan numbers and the number of standard Young tableaux of shape(1,2,...,n). 1
1, 1, 4, 160, 107520, 1722040320, 854352419880960, 16185399027773630054400, 13931397052191274338996977664000, 632089112919018408339999461491467091968000, 1721041721929360607907210006858724622834371563356160000 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A224198 A104133 A214007 * A157463 A041779 A222394
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 24 01:57 EDT 2024. Contains 374575 sequences. (Running on oeis4.)