A174160 A symmetrical triangular sequence:t(n,m)=2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2

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

Offset

1,8

Comments

Row sums are:

{1, 2, 1, -26, -362, -4012, -43479, -477962, -5380274, -62040980,...}.

Links

Table of n, a(n) for n=1..47.

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

Cf. A001263, A008292

Sequence in context: A373160 A206564 A076158 * A199256 A199201 A128883

Adjacent sequences: A174157 A174158 A174159 * A174161 A174162 A174163

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 10 2010

Status

approved