A178046 Triangle t(n, m) = 2*binomial(n,m)^2 -A008292(n+1,m+1)^2 read by rows.

1, 1, 1, 1, -8, 1, 1, -103, -103, 1, 1, -644, -4284, -644, 1, 1, -3199, -91004, -91004, -3199, 1, 1, -14328, -1418031, -5836256, -1418031, -14328, 1, 1, -60911, -18428967, -243950711, -243950711, -18428967, -60911, 1, 1, -251876

Offset: 0

Author

Roger L. Bagula, May 18 2010

Keywords

• sign
• tabl

Comments

Row sums are A028329(n) - A168562(n+1). - R. J. Mathar, Nov 05 2012

Examples

			1;
1, 1;
1, -8, 1;
1, -103, -103, 1;
1, -644, -4284, -644, 1;
1, -3199, -91004, -91004, -3199, 1;
1, -14328, -1418031, -5836256, -1418031, -14328, 1;
1, -60911, -18428967, -243950711, -243950711, -18428967, -60911, 1;
1, -251876, -213392096, -7785232484, -24395306300, -7785232484, -213392096, -251876, 1;
		

Crossrefs

Cf. A177823, A008459, A141686, A008292

Programs

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] = 2*Binomial[n, m]^2 - Eulerian[n + 1, m]^2;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]