A208631 - OEIS

A208631

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

%I #17 Jan 28 2019 17:12:23

%S 1,1,3,53,25187,705002611,1672481205752413,475092942773985252468181,

%T 22081439406257212482754663652213531,

%U 220381419513554767061883905294847700173775763891,599868749018773480515945947095662848011697924400242771204050409

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

%C Also the number of (n^2-1)-step walks on n-dimensional cubic lattice from (1,0,...,0) to (n,n,...,n) with positive unit steps in all dimensions such that for each point (p_1,p_2,...,p_n) we have p_1<=p_2<=...<=p_n or p_1>=p_2>=...>=p_n.

%H Alois P. Heinz, <a href="/A208631/b208631.txt">Table of n, a(n) for n = 0..12</a>

%Y Main diagonal of A208615.

%K nonn,walk

%O 0,3

%A _Alois P. Heinz_, Feb 29 2012