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Number of Young tableaux with 4 n-length rows, increasing entries down the columns and monotonic entries along the rows (first row increasing).
1

%I #12 Jan 08 2013 11:16:21

%S 1,1,35,587,25187,1676707,140422657,13675362559,1489926719139,

%T 177296325559211,22661600612752505,3073259866183533755,

%U 438091469007903238421,65166105272787401522141,10056663348255976399237441,1602608180008201242503733271

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

%C Also the number of (4*n-1)-step walks on n-dimensional cubic lattice from (1,0,...,0) to (4,4,...,4) 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.

%Y Row n=4 of A208615.

%K nonn,walk

%O 0,3

%A _Alois P. Heinz_, Feb 29 2012