A162498 Triangle read by rows: T(n, k) = Sum_{j=0..k} (-1)^j*binomial(n, j)*(k + 1 - j)^(n - 1).

1, 1, 1, 3, 4, 1, 23, 33, 11, 1, 425, 620, 220, 26, 1, 18129, 26525, 9520, 1180, 57, 1, 1721419, 2519664, 905765, 113050, 5649, 120, 1, 353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1, 153923102577, 225309742552, 81009042744, 10119247684, 507795498, 11059468, 109386, 502, 1

Offset: 1

Author

Roger L. Bagula and Mats Granvik, Dec 06 2009

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins:
  {1},
  {1, 1},
  {3, 4, 1},
  {23, 33, 11, 1},
  {425, 620, 220, 26, 1},
  {18129, 26525, 9520, 1180, 57, 1},
  {1721419, 2519664, 905765, 113050, 5649, 120, 1},
  {353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1},
  {153923102577, 225309742552, 81009042744, 10119247684, 507795498, 11059468, 109386, 502, 1},
  ...
		

Crossrefs

Cf. A154921. An unsigned version of A055325.

Programs

Mathematica

t[n_,k_]:=Sum[(-1)^j Binomial[n,j](k+1-j)^(n-1),{j,0,k}];
M[n_]:=Table[If[k <= m,(-1)^(m+k)*t[m,k],0],{k,0,n-2},{m,2,n}];
Flatten[Table[Table[Inverse[M[12]][[m,n]],{m,1,n}],{n,1,11}]]