0,4

Triangle begins:

1;

1, 1;

2, 2, 1;

12, 8, 3, 1;

156, 80, 20, 4, 1;

3540, 1516, 300, 40, 5, 1;

123400, 46236, 7816, 840, 70, 6, 1;

6091988, 2054980, 309268, 28816, 1960, 112, 7, 1;

402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1; ...

Matrix square T^2 begins:

1;

2, 1;

6, 4, 1;

38, 22, 6, 1;

480, 232, 52, 8, 1; ...

[Row 2 of T] = [row 1 of T^2, 0] + [0, row 1 of T]:

[2, 2, 1] = [2, 1, 0] + [0, 1, 1].

Matrix cube T^3 begins:

1;

3, 1;

12, 6, 1; ...

[Row 3 of T] = [row 2 of T^3, 0] + [0, row 2 of T]:

[12, 8, 3, 1] = [12, 6, 1, 0] + [0, 2, 2, 1].

Matrix 4-th power T^4 begins:

1;

4, 1;

20, 8, 1;

156, 68, 12, 1; ...

[Row 4 of T] = [row 3 of T^4, 0] + [0, row 3 of T]:

[156, 80, 20, 4, 1] = [156, 68, 12, 1, 0] + [0, 12, 8, 3, 1].

(PARI) {T(n, k)=local(M=Mat(1)); if(n<k|k<0, 0, if(n==k, 1, M=matrix(n+1, n+1, r, c, if(n==k, 1, if(r>=c&r<=n, T(r-1, c-1)))); T(n-1, k-1)+(M^n)[n, k+1]))}

Columns: A130529, A130530, A130531.

Sequence in context: A014846 A100942 A132471 this_sequence A132986 A019112 A048660

Adjacent sequences: A130525 A130526 A130527 this_sequence A130529 A130530 A130531

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 02 2007