OFFSET
1,2
COMMENTS
The matrix inverse starts:
1;
-2, 1;
-3, -1, 1;
-8, -1, -1, 1;
-31, -3, 0, -1, 1;
-132, -7, -1, 0, -1, 1;
-616, -19, -4, 0, 0, -1, 1; - R. J. Mathar, Mar 22 2013
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
N. J. A. Sloane, Transforms
FORMULA
T(n,k) = Sum_{j=0..n-k} C(n-k,j)*T(j,k) if n>=k, else T(n,k) = 1 if n=1, else T(n,k) = 0.
EXAMPLE
T(5,2) = 5, because [1,3,3,1] * [1,0,1,1] = 5.
Triangle begins:
: 1;
: 2, 1;
: 5, 1, 1;
: 15, 2, 1, 1;
: 52, 5, 1, 1, 1;
: 203, 13, 2, 1, 1, 1;
: 877, 36, 6, 1, 1, 1, 1;
: 4140, 109, 17, 2, 1, 1, 1, 1;
: 21147, 359, 44, 7, 1, 1, 1, 1, 1;
: 115975, 1266, 112, 23, 2, 1, 1, 1, 1, 1;
MAPLE
T:= proc(n, k) option remember; `if`(n<k, `if`(n=0, 1, 0),
add(binomial(n-k, j) *T(j, k), j=0..n-k))
end:
seq(seq(T(n, k), k=1..n), n=1..14);
MATHEMATICA
t[n_, k_] := t[n, k] = If[n < k, If[n == 0, 1, 0], Sum[Binomial[n-k, j]*t[j, k], {j, 0, n-k}]]; Table[Table[t[n, k], {k, 1, n}], {n, 1, 13}] // Flatten (* Jean-François Alcover, Dec 18 2013, translated from Maple *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Sep 06 2008
STATUS
approved