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T05

T_{5}(n,k)= \binom{n}{k}(-2)^{n-k}E_{n-k}(1/2)

Triangular form
1  
0 1  
-1 0 1  
0 -3 0 1  
5 0 -6 0 1  
0 25 0 -10 0 1  
-61 0 75 0 -15 0 1
sum als gcd lcm
1 1 1 1
1 1 1 1
2 2 1 1
4 4 3 3
12 12 1 30
36 36 5 50
152 152 1 4575
Linear form (by rows)
Western A119879 1,0,1,-1,0,1,0,-3,0,1,5,0,-6,0,1
Eastern A000000 1,1,0,1,0,-1,1,0,-3,0,1,0,-6,0,5
Rectangular form
1 0 -1 0 5 0 -61
1 0 -3 0 25 0 -427
1 0 -6 0 75 0 -1708
1 0 -10 0 175 0 -5124
1 0 -15 0 350 0 -12810
1 0 -21 0 630 0 -28182
1 0 -28 0 1050 0 -56364
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Sub Seq 0 1 2 3
Row A122045 A104033 A086646 A104033
Col A000012 A000004 A000217 A000004
RowDiag A086646 A104033 A086646 A104033
ColDiag A086646 A104033 A086646 A104033
Characteristic SUM ALS LCM GCD
A003701 A003701 A000000 A155457
  MIN MAX CENTRAL MIDDLE
A000000 A000000 A000000 A000000

Maple T05 := proc(n, k) binomial(n,k)*(-2)^(n-k)*euler(n-k,1/2) end:

TeX T_{5}(n,k)= \binom{n}{k}(-2)^{n-k}E_{n-k}(1/2)