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T01

T_{1}(n, k) = \binom{n}{k}

Triangular form
1  
1 1  
1 2 1  
1 3 3 1  
1 4 6 4 1  
1 5 10 10 5 1  
1 6 15 20 15 6 1
sum als gcd lcm
1 1 1 1
2 0 1 1
4 0 2 2
8 0 3 3
16 0 2 12
32 0 5 10
64 0 1 60
Linear form (by rows)
Western A007318 1,1,1,1,2,1,1,3,3,1
Eastern A007318 1,1,1,1,2,1,1,3,3,1
Rectangular form
1 1 1 1 1 1 1
1 2 3 4 5 6 7
1 3 6 10 15 21 28
1 4 10 20 35 56 84
1 5 15 35 70 126 210
1 6 21 56 126 252 462
1 7 28 84 210 462 924
Fingerprint
Sub Seq 0 1 2 3
Row A000012 A000027 A000217 A000292
Col A000012 A000027 A000217 A000292
RowDiag A000984 A001700 A001791 A002054
ColDiag A000984 A001700 A001791 A002054
Characteristic SUM ALS LCM GCD
  A000079 A000007 A002944 A014963
  MIN MAX CENTRAL MIDDLE
A000012 A001405 A000984 A001405

Maple T01 := proc(n,k) binomial(n,k) end:

TeX T_{1}(n, k) = \binom{n}{k}