A141690 Triangle t(n,m) = 2*A008292(n+1,m+1) - A007318(n,m), a linear combination of Eulerian numbers and Pascal's triangle, 0 <= m <= n.

1, 1, 1, 1, 6, 1, 1, 19, 19, 1, 1, 48, 126, 48, 1, 1, 109, 594, 594, 109, 1, 1, 234, 2367, 4812, 2367, 234, 1, 1, 487, 8565, 31203, 31203, 8565, 487, 1, 1, 996, 29188, 176412, 312310, 176412, 29188, 996, 1, 1, 2017, 95644, 910300, 2620582, 2620582, 910300

Offset: 0

Author

Roger L. Bagula, Sep 09 2008

Keywords

• nonn
• tabl

Comments

Row sums are 1, 2, 8, 40, 224, 1408, 10016, 80512, 725504, 7257088, ... = 2*(n+1)! - 2^n.

Examples

			Triangle begins
  1;
  1,    1;
  1,    6,     1;
  1,   19,    19,      1;
  1,   48,   126,     48,       1;
  1,  109,   594,    594,     109,       1;
  1,  234,  2367,   4812,    2367,     234,      1;
  1,  487,  8565,  31203,   31203,    8565,    487,     1;
  1,  996, 29188, 176412,  312310,  176412,  29188,   996,    1;
  1, 2017, 95644, 910300, 2620582, 2620582, 910300, 95644, 2017, 1;
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A008292, A007318.

Programs

Maple

A141690 := proc(n,m)
        2*A008292(n+1,m+1)-binomial(n,m) ;
end proc: # R. J. Mathar, Jul 12 2012

Mathematica

Table[Table[(2*Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] - Binomial[n - 1, k]), {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]