OFFSET
0,5
COMMENTS
FORMULA
EXAMPLE
Rows of T begin:
[1],
[1,1],
[0,2,1],
[0,2,4,1],
[0,2,12,8,1],
[0,2,44,56,16,1],
[0,2,236,504,240,32,1],
[0,2,2028,6776,4720,992,64,1],
[0,2,29164,146552,139120,40672,4032,128,1],
[0,2,719340,5314680,6583152,2500832,337344,16256,256,1],...
Rows of T^2 begin:
[1],
[2,1],
[2,4,1],
[2,12,8,1],
[2,44,56,16,1],
[2,236,504,240,32,1],...
showing that T shifts left and up under matrix square.
The matrix inverse of T begins:
[1],
[ -1,1],
[2,-2,1],
[ -6,6,-4,1],
[26,-26,20,-8,1],
[ -166,166,-140,72,-16,1],...
the absolute value of which equals triangle A098539.
PROG
(PARI) T(n, k)=local(A, B); A=matrix(1, 1); A[1, 1]=1; for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, B[i, j]=1, if(j==1, B[i, j]=(A^0)[i-1, 1], B[i, j]=(A^2)[i-1, j-1])); )); A=B); A[n+1, k+1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Sep 16 2004
STATUS
approved