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).

1, 2, 3, 4, 7, 20, 107, 1251, 39449, 3601484, 993083163, 822645013440, 2233613397459767, 19448649149110190799, 611288282025228989179209, 65375294476542363327381312458, 27613527789685567969428106708416272, 41649724056091694466822995563486395949185

Offset: 0

Author

Alois P. Heinz, Mar 01 2012

Keywords

• nonn
• walk

Comments

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..25

Crossrefs

Antidiagonal sums of A208615.