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A208729 Number of Young tableaux with i k-length rows with i,k>=0, i+k=n, increasing entries down the columns and monotonic entries along the rows (first row increasing).

%I A208729 #11 Sep 07 2016 18:35:00
%S A208729 1,2,3,4,7,20,107,1251,39449,3601484,993083163,822645013440,
%T A208729 2233613397459767,19448649149110190799,611288282025228989179209,
%U A208729 65375294476542363327381312458,27613527789685567969428106708416272,41649724056091694466822995563486395949185
%N A208729 Number of Young tableaux with i k-length rows with i,k>=0, i+k=n, increasing entries down the columns and monotonic entries along the rows (first row increasing).
%C A208729 a(n) is also the number of (i*k-1)-step walks (for all i,k>=0, i+k=n) on k-dimensional cubic lattice from (1,0,...,0) to (i,i,...,i) with positive unit steps in all dimensions such that for each point (p_1,p_2,...,p_k) we have p_1<=p_2<=...<=p_k or p_1>=p_2>=...>=p_k.
%H A208729 Alois P. Heinz, <a href="/A208729/b208729.txt">Table of n, a(n) for n = 0..25</a>
%Y A208729 Antidiagonal sums of A208615.
%K A208729 nonn,walk
%O A208729 0,2
%A A208729 _Alois P. Heinz_, Mar 01 2012