A208624 Number of Young tableaux with n 4-length rows, increasing entries down the columns and monotonic entries along the rows (first row increasing).

1, 1, 15, 491, 25187, 1725819, 144558247, 14029729645, 1523926182363, 180929760551225, 23086562828397479, 3126799551978895629, 445266632168280620515, 66178991463387525289801, 10206120232877820185701707, 1625518539321873371313790283

Offset: 0

Author

Alois P. Heinz, Feb 29 2012

Keywords

• nonn
• walk

Comments

Also the number of (4*n-1)-step walks on 4-dimensional cubic lattice from (1,0,0,0) to (n,n,n,n) with positive unit steps in all dimensions such that for each point (p_1,p_2,p_3,p_4) we have p_1<=p_2<=p_3<=p_4 or p_1>=p_2>=p_3>=p_4.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Column k=4 of A208615.

Formula

a(n) ~ c * 256^n / n^(15/2), where c = 1.536590923866647845196812662963243246... . - Vaclav Kotesovec, Sep 03 2014