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T02

T_{2}(n, k) = \sum_{j=0}^{k}\frac{(-1)^{k-j}}{k+1}\binom{k+1}{j+1}(j+1)^{n+1}

TriangleForm
1  
1 1  
1 3 2  
1 7 12 6  
1 15 50 60 24  
1 31 180 390 360 120  
1 63 602 2100 3360 2520 720
sum als gcd lcm
1 1 0 1
2 0 0 1
6 0 1 6
26 0 1 84
150 0 1 600
1082 0 1 145080
9366 0 1 2167200
RectangleForm
1 1 1 1 1 1 1
1 3 7 15 31 63 127
2 12 50 180 602 1932 6050
6 60 390 2100 10206 46620 204630
24 360 3360 25200 166824 1020600 5921520
120 2520 31920 317520 2739240 21538440 158838240
720 20160 332640 4233600 46070640 451725120 4115105280
Fingerprint
SubSeqType 0 1 2 3
Row A000012 A000225 A028243 A028245
Column A000142 A001710 A005460 A005461
DiagRow A000000 A000000 A000000 A000000
DiagColumn A000000 A000000 A000000 A000000
Characteristic SUM ALS LCM GCD
Sequence A000629 A000007 A000000 A000000

Maple T02 := proc(n,k) local i; (1/(k+1))*add((-1)^(k-i)*binomial(k+1,i+1)*(i+1)^(n+1),i=0..k) end:

TeX T_{2}(n, k) = \sum_{j=0}^{k}\frac{(-1)^{k-j}}{k+1}\binom{k+1}{j+1}(j+1)^{n+1}