A117398 Matrix log of triangle A117396.
0, 1, 0, 0, 2, 0, -1, 2, 3, 0, -3, 4, 5, 4, 0, -9, 14, 15, 9, 5, 0, -33, 68, 65, 34, 14, 6, 0, -153, 404, 359, 174, 63, 20, 7, 0, -873, 2804, 2375, 1098, 371, 104, 27, 8, 0, -5913, 22244, 18215, 8154, 2639, 692, 159, 35, 9, 0, -46233, 198644, 158615, 69354, 21791, 5480, 1179, 230, 44, 10, 0
Offset: 0
Examples
Triangle begins:
0;
1, 0;
0, 2, 0;
-1, 2, 3, 0;
-3, 4, 5, 4, 0;
-9, 14, 15, 9, 5, 0;
-33, 68, 65, 34, 14, 6, 0;
-153, 404, 359, 174, 63, 20, 7, 0;
-873, 2804, 2375, 1098, 371, 104, 27, 8, 0;
-5913, 22244, 18215, 8154, 2639, 692, 159, 35, 9, 0;
Links
- G. C. Greubel, Rows n = 0..50 of the triangle, flattened
Programs
-
Mathematica
m=12; M= Table[If[k>n-1, 0, If[k==n-1, n, -1]], {n,0,m+1}, {k,0,m+1}]; T:= T= Sum[MatrixPower[M, j]/j, {j,m+1}]; Table[T[[n+1, k+1]], {n,0,m}, {k,0,n}]//Flatten (* G. C. Greubel, Sep 06 2022 *) -
PARI
{T(n,k)=local(M=matrix(n+4,n+4,r,c,if(r>=c,if(r==c+1,-c,1))), L=sum(m=1,n+4,(M^0-M)^m/m));L[n+1,k+1]}
Comments