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A141681
The matrix inverse of the triangle A141680.
1
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
1,2
COMMENTS
Row sums are 1, -3, -8, 21, -24, 420, -48, -2667, 1936, 12672, ...
FORMULA
Sum_{j=k..n} T(n,j) * A141680(j,k) = delta(n,k).
EXAMPLE
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;
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[%]
CROSSREFS
Cf. A126988.
Sequence in context: A360131 A177841 A141680 * A176215 A364016 A143469
KEYWORD
tabl,sign
AUTHOR
STATUS
approved