OFFSET
0,4
COMMENTS
A triangle having similar properties and complementary construction is the dual triangle A098568.
FORMULA
Remarkably, row n of the matrix inverse (A121438) equals row n of A121412^(-n*(n+1)/2). Further, the following matrix products of triangles of binomial coefficients are equal: A121412 = A121334*A122178^-1 = A121335*A121334^-1 = A121336*A121335^-1, where row n of H=A121412 equals row (n-1) of H^(n+1) with an appended '1'.
EXAMPLE
Triangle begins:
1;
1, 1;
6, 3, 1;
56, 21, 6, 1;
715, 220, 55, 10, 1;
11628, 3060, 680, 120, 15, 1;
230230, 53130, 10626, 1771, 231, 21, 1;
5379616, 1107568, 201376, 31465, 4060, 406, 28, 1;
145008513, 26978328, 4496388, 658008, 82251, 8436, 666, 36, 1; ...
PROG
(PARI) T(n, k)=binomial(n*(n+1)/2+n-k-1, n-k)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Aug 29 2006
STATUS
approved