A141681 The matrix inverse of the triangle A141680.
1, -4, 1, -9, 0, 1, 32, -12, 0, 1, -25, 0, 0, 0, 1, 504, -45, -40, 0, 0, 1, -49, 0, 0, 0, 0, 0, 1, -4096, 1568, 0, -140, 0, 0, 0, 1, 2187, 0, -252, 0, 0, 0, 0, 0, 1, 13400, -225, 0, 0, -504, 0, 0, 0, 0, 1, -121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 1
Examples
Triangle begins
1;
-4, 1;
-9, 0, 1;
32, -12, 0, 1;
-25, 0, 0, 0, 1;
504, -45, -40, 0, 0, 1;
-49, 0, 0, 0, 0, 0, 1;
-4096, 1568, 0, -140, 0, 0, 0, 1;
2187, 0, -252, 0, 0, 0, 0, 0, 1;
13400, -225, 0, 0, -504, 0, 0, 0, 0, 1;
Links
- G. C. Greubel, Rows n=1..100 of triangle, flattened
Crossrefs
Cf. A126988.
Programs
-
Mathematica
t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]*Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]; Table[Sum[t[n, m], {m, 1, n}], {n, 1, 10}]; M = Inverse[Table[Table[t[n, m], {m, 1, 10}], {n, 1, 10}]]; Table[Table[M[[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[%]
Formula
Sum_{j=k..n} T(n,j) * A141680(j,k) = delta(n,k).
Comments