A091614 Matrix inverse of triangle A091613.

1, -1, 1, -3, 0, 1, -1, -3, 0, 1, 5, -6, -2, 0, 1, 13, -4, -5, -2, 0, 1, 27, 1, -7, -4, -2, 0, 1, 41, 12, -4, -6, -4, -2, 0, 1, 43, 35, 4, -6, -5, -4, -2, 0, 1, 25, 72, 18, 0, -5, -5, -4, -2, 0, 1, -23, 128, 40, 11, -2, -4, -5, -4, -2, 0, 1, -157, 205, 77, 30, 8, -1, -4, -5, -4, -2, 0, 1

Offset: 1

Author

Christian G. Bower, Jan 23 2004

Keywords

• sign
• tabl

Examples

			Triangle begins as:
    1;
   -1,   1;
   -3,   0,  1;
   -1,  -3,  0,  1;
    5,  -6, -2,  0,  1;
   13,  -4, -5, -2,  0,  1;
   27,   1, -7, -4, -2,  0,  1;
   41,  12, -4, -6, -4, -2,  0,  1;
   43,  35,  4, -6, -5, -4, -2,  0,  1;
   25,  72, 18,  0, -5, -5, -4, -2,  0,  1;
  -23, 128, 40, 11, -2, -4, -5, -4, -2,  0,  1;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A091613, A091623 (first column).

Programs

Mathematica

b[n_, l_, k_]:= b[n, l, k]= If[n==0, 1, Sum[If[i==l, 0, Sum[b[n-i*j, i, k], {j, Min[k, n/i]}]], {i, n}]];
t[n_, k_]:= b[n, 0, k] - b[n, 0, k-1]; (* t = A091613 *)
M:= With[{p = 16}, Table[t[n, k], {n, p}, {k, p}]];
T:= Inverse[M];
Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Nov 27 2021 *)

Extensions

Name corrected by G. C. Greubel, Nov 27 2021