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

0,3

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

Formula

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

Crossrefs

Column k=4 of A208615.

Sequence in context: A252929 A218198 A377045 * A013433 A013435 A151816

Adjacent sequences: A208621 A208622 A208623 * A208625 A208626 A208627

Keyword

nonn,walk

Author

Alois P. Heinz, Feb 29 2012

Status

approved