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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). 2
1, 2, 3, 4, 7, 20, 107, 1251, 39449, 3601484, 993083163, 822645013440, 2233613397459767, 19448649149110190799, 611288282025228989179209, 65375294476542363327381312458, 27613527789685567969428106708416272, 41649724056091694466822995563486395949185 (list; graph; refs; listen; history; text; internal format)
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: A139439 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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)