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T11

T_{11}(n,k) = \frac{1}{k+1} \binom{n}{k}\binom{n-1}{k}

TriangleForm
1  
1 0  
1 1 0  
1 3 1 0  
1 6 6 1 0  
1 10 20 10 1 0  
1 15 50 50 15 1 0
sum als gcd lcm
1 1 0 1
1 1 0 1
2 0 0 1
5 1 3 3
14 0 6 6
42 2 10 20
132 0 5 150
RectangleForm
1 1 1 1 1 1 1
0 1 3 6 10 15 21
0 1 6 20 50 105 196
0 1 10 50 175 490 1176
0 1 15 105 490 1764 5292
0 1 21 196 1176 5292 19404
0 1 28 336 2520 13860 60984
Fingerprint
SubSeqType 0 1 2 3
Row A000012 A000217 A002415 A006857
Column A000007 A000012 A000217 A002415
DiagRow A125558 A000000 A000000 A000000
DiagColumn A125558 A000891 A125558 A000000
Characteristic SUM ALS LCM GCD
Sequence A000108 A105523 A000000 A000000

Maple T11 := proc(n,k) binomial(n,k)*binomial(n-1,k)/(k+1) end:

TeX T_{11}(n,k) = \frac{1}{k+1} \binom{n}{k}\binom{n-1}{k}