A176862 A symmetrical triangle sequence:t(n,m)=(-1)^m*(n - m)!*Binomial[n - 1, m] + (-1)^(n - m + 1)*(n - (n - m + 1))!*Binomial[n - 1, n - m + 1].

2, 5, 5, 37, -16, 37, 239, -50, -50, 239, 1801, -492, 180, -492, 1801, 15119, -4186, 714, 714, -4186, 15119, 141121, -40336, 8568, -2688, 8568, -40336, 141121, 1451519, -423342, 90504, -13104, -13104, 90504, -423342, 1451519

Offset: 3

Author

Roger L. Bagula, Apr 27 2010

Keywords

• sign
• tabl
• uned

Comments

Row sums are:

{2, 10, 58, 378, 2798, 23294, 216018, 2211154,...}.

Examples

			{2},
{5, 5},
{37, -16, 37},
{239, -50, -50, 239},
{1801, -492, 180, -492, 1801},
{15119, -4186, 714, 714, -4186, 15119},
{141121, -40336, 8568, -2688, 8568, -40336, 141121},
{1451519, -423342, 90504, -13104, -13104, 90504, -423342, 1451519}
		

References

• F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 576 and 270.

Crossrefs

Cf. A132159

Programs

Mathematica

t[n_, m_] := (-1)^m*(n - m)!*Binomial[n - 1, m] + (-1)^(n - m + 1)*(n - (n - m + 1))!*Binomial[n - 1, n - m + 1];
Table[Table[t[n, m], {m, 2, n - 1}], {n, 3, 10}];
Flatten[%]

Formula

t(n,m)=(-1)^m*(n - m)!*Binomial[n - 1, m] + (-1)^(n - m + 1)*(n - (n - m + 1))!*Binomial[n - 1, n - m + 1]