A141903 A linear combination of A008292 and A130595: t(n,m)=2*A008292(n,m)- A130595(n,m).

1, 1, 3, 1, 10, 1, 1, 25, 19, 3, 1, 56, 126, 56, 1, 1, 119, 594, 614, 109, 3, 1, 246, 2367, 4852, 2367, 246, 1, 1, 501, 8565, 31273, 31203, 8607, 487, 3, 1, 1012, 29188, 176524, 312310, 176524, 29188, 1012, 1, 1, 2035, 95644, 910468, 2620582, 2620834, 910300

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 14 2008

Keywords

• nonn
• uned

Comments

Row sums are:

{1, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600}.

Examples

			{1},
{1, 3},
{1, 10, 1},
{1, 25, 19, 3},
{1, 56, 126, 56, 1},
{1, 119, 594, 614, 109, 3},
{1, 246, 2367, 4852, 2367, 246, 1},
{1, 501, 8565, 31273, 31203, 8607, 487, 3},
{1, 1012, 29188, 176524, 312310, 176524, 29188, 1012, 1},
{1, 2035, 95644, 910468, 2620582, 2620834, 910300, 95716, 2017, 3}
		

Crossrefs

Cf. A008292 and A130595.

Programs

Mathematica

A[n_, 1] := 1 A[n_, n_] := 1 A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + k A[n - 1, k]; Table[Table[2*A[n, k] - (-1)^(k + 1)*Binomial[n - 1, k - 1], {k, 1, n}], {n, 1, 10}]; Flatten[%]

Formula

t(n,m)=2*A008292(n,m)- A130595(n,m).