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T14

T_{14}(n,k)= \sum_{j=0}^k (-1)^j\binom{n+1}{j}(2(k-j)+1)^n

TriangleForm
1  
1 1  
1 6 1  
1 23 23 1  
1 76 230 76 1  
1 237 1682 1682 237 1  
1 722 10543 23548 10543 722 1
sum als gcd lcm
1 1 0 1
2 0 0 1
8 4 6 6
48 0 23 23
384 80 2 8740
3840 0 1 398634
46080 3904 1 89624229604
RectangleForm
1 1 1 1 1 1 1
1 6 23 76 237 722 2179
1 23 230 1682 10543 60657 331612
1 76 1682 23548 259723 2485288 21707972
1 237 10543 259723 4675014 69413294 906923282
1 722 60657 2485288 69413294 1527092468 28588019814
1 2179 331612 21707972 906923282 28588019814 743288515164
Fingerprint
SubSeqType 0 1 2 3
Row A000012 A060188 A060189 A060190
Column A000012 A060188 A060189 A060190
DiagRow A000000 A000000 A000000 A000000
DiagColumn A000000 A000000 A000000 A000000
Characteristic SUM ALS LCM GCD
Sequence A000165 A002436 A000000 A000000

Maple T14 := proc(n, k) local j; add((-1)^j*binomial(n+1,j)*(2*(k-j)+1)^n,j=0..k) end:

TeX T_{14}(n,k)= \sum_{j=0}^k (-1)^j\binom{n+1}{j}(2(k-j)+1)^n