OFFSET
1,8
COMMENTS
Row sums are:
{1, 2, 1, -26, -362, -4012, -43479, -477962, -5380274, -62040980,...}.
FORMULA
t(n,m)=2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2
EXAMPLE
{1},
{1, 1},
{1, -1, 1},
{1, -14, -14, 1},
{1, -48, -268, -48, 1},
{1, -111, -1896, -1896, -111, 1},
{1, -201, -8643, -25793, -8643, -201, 1},
{1, -290, -29830, -208862, -208862, -29830, -290, 1},
{1, -292, -83680, -1206508, -2799316, -1206508, -83680, -292, 1},
{1, 1, -195920, -5440016, -25384556, -25384556, -5440016, -195920, 1, 1}
MATHEMATICA
<< DiscreteMath`Combinatorica`
t[n_, m_] =2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2;
Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 10 2010
STATUS
approved