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

0,2

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.

Sequence in context: A352902 A119330 A084644 * A270777 A100686 A052340

Adjacent sequences: A208726 A208727 A208728 * A208730 A208731 A208732

Keyword

nonn,walk

Author

Alois P. Heinz, Mar 01 2012

Status

approved