A130671 Triangular sequence based on Pascal's triangle: t(n,m) = 2*binomial(m, n) - (1 + n*(m - n)).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 21, 30, 21, 6, 1, 1, 7, 31, 57, 57, 31, 7, 1, 1, 8, 43, 96, 123, 96, 43, 8, 1, 1, 9, 57, 149, 231, 231, 149, 57, 9, 1, 1, 10, 73, 218, 395, 478, 395, 218, 73, 10, 1

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Jun 27 2007

Keywords

• nonn
• tabl

Comments

Suggested by Gary W. Adamson from a previous submission. Very close to (but slightly smaller at 7th row) A086617.

Examples

			{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 7, 4, 1},
{1, 5, 13, 13, 5, 1},
{1, 6, 21, 30, 21, 6, 1},
{1, 7, 31, 57, 57, 31, 7, 1}
		

Crossrefs

Cf. A086617.

Programs

Mathematica

Table[Table[2*Binomial[m, n] - (1 + n*(m - n)), {n, 0, m}], {m, 0, 10}] Flatten[%]

Formula

t(n,m) = 2*binomial[m, n] - (1 + n*(m - n)).