A159881 Triangle read by rows : T(n,0) = n+1, T(n,k)=0 if k<0 or if k>n, T(n,k) = k*T(n-1,k) - T(n-1,k-1).

1, 2, -1, 3, -3, 1, 4, -6, 5, -1, 5, -10, 16, -8, 1, 6, -15, 42, -40, 12, -1, 7, -21, 99, -162, 88, -17, 1, 8, -28, 219, -585, 514, -173, 23, -1, 9, -36, 466, -1974, 2641, -1379, 311, -30, 1, 10, -45, 968, -6388, 12538, -9536, 3245, -521, 38, -1

Offset: 0

Author

Philippe Deléham, Apr 25 2009

Keywords

• easy
• sign
• tabl

Examples

			Triangle begins :
1;
2, -1;
3, -3, 1;
4, -6, 5, -1;
5, -10, 16, -8, 1;
6, -15, 42, -40, 12, -1;
7, -21, 99, -162, 88, -17, 1;
8, -28, 219, -585, 514, -173, 23, -1;
9, -36, 466, -1974, 2641, -1379, 311, -30, 1;
10, -45, 968, -6388, 12538, -9536, 3245, -521, 38, -1;
11, -55, 1981, -20132, 56540, -60218, 29006, -6892, 825, -47, 1;
		

Links

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

Crossrefs

Cf. A000027, A000217, A002662, A152948

Programs

Maple

A159881 := proc(n,k) option remember; if k = 0 then n+1; elif k < 0 or k > n then 0 ; else k*procname(n-1,k)-procname(n-1,k-1) ; fi; end: for n from 0 to 10 do for k from 0 to n do printf("%d,",A159881(n,k)) ; od: od: # R. J. Mathar, May 29 2009

Mathematica

T[n_,0]:= n+1; T[n_,k_]:= T[n,k] = If[k < 0 || k > n, 0, k*T[n-1, k] - T[n-1, k-1]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 27 2018 *)

PARI

{T(n,k) = if(k==0, n+1, if(k<0 || k>n, 0, k*T(n-1,k) - T(n-1,k-1)))};
for(n=0,15, for(k=0,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Jul 27 2018

Formula

Conjecture row sums: Sum_{k=0..n} |T(n,k)| = A029761(n). - R. J. Mathar, May 29 2009