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T07

T_{07}(n,k)=\binom{n}{k}2^{n-k}(E_{n-k}(1/2)+E_{n-k}(1))

Triangular form
1  
1 0  
-1 2 0  
-2 -3 3 0  
5 -8 -6 4 0  
16 25 -20 -10 5 0  
-61 96 75 -40 -15 6 0
sum als gcd lcm
0 0 0 1
1 1 0 1
3 1 1 2
8 2 1 6
23 1 1 120
76 6 1 400
293 9 1 146400
Linear form (by rows)
Western A173018 1,1,0,1,1,0,1,4
Eastern A123125 1,0,1,0,1,1,0,1
Rectangular form
0 1 -1 -2 5 16 -61
0 2 -3 -8 25 96 -427
0 3 -6 -20 75 336 -1708
0 4 -10 -40 175 896 -5124
0 5 -15 -70 350 2016 -12810
0 6 -21 -112 630 4032 -28182
0 7 -28 -168 1050 7392 -56364
Fingerprint
Sub Seq 0 1 2 3
Row A000111 A065619 A000000 A000000
Col A000012 A000027 A000217 A007290
RowDiag A000000 A000000 A000000 A000000
ColDiag A000000 A000000 A000000 A000000
Characteristic SUM ALS LCM GCD
  A000667 A062162 A000000 A000000
  MIN MAX CENTRAL MIDDLE
A000007 A009006 A180056 A009006

Maple T07 := proc(n,k) binomial(n,k)*2^(n-k)*(euler(n-k,1/2)+euler(n-k,1)) end:

TeX T_{07}(n,k)=\binom{n}{k}2^{n-k}(E_{n-k}(1/2)+E_{n-k}(1))