A373967 Triangle read by rows: T(n,k) = (-1)^n * n! + (-1)^(k+1) * k! for n >= 2 and 1 <= k <= n-1.

3, -5, -8, 25, 22, 30, -119, -122, -114, -144, 721, 718, 726, 696, 840, -5039, -5042, -5034, -5064, -4920, -5760, 40321, 40318, 40326, 40296, 40440, 39600, 45360, -362879, -362882, -362874, -362904, -362760, -363600, -357840, -403200, 3628801, 3628798, 3628806, 3628776, 3628920, 3628080, 3633840, 3588480, 3991680

Offset: 2

Author

Mohammed Yaseen, Jun 24 2024

Keywords

• sign
• tabl
• easy

Examples

			Triangle begins:
      3;
     -5,    -8;
     25,    22,    30;
   -119,  -122,  -114,  -144;
    721,   718,   726,   696,   840;
  -5039, -5042, -5034, -5064, -4920, -5760;
  ...
		

Crossrefs

Cf. A000142, A153805, A373966.

Unsigned diagonals: A001048, A213167.

Programs

Mathematica

T[n_,k_]:= (-1)^n*n! + (-1)^(k+1)*k!; Table[T[n,k],{n,2,10},{k,n-1}]// Flatten (* Stefano Spezia, Jun 24 2024 *)

Formula

Integral_{1..e} (log(x)^k - log(x)^n) dx = A373966(n,k)*e + T(n,k).