login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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).
2
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
0,2
FORMULA
Conjecture row sums: Sum_{k=0..n} |T(n,k)| = A029761(n). - R. J. Mathar, May 29 2009
EXAMPLE
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;
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,sign,tabl
AUTHOR
Philippe Deléham, Apr 25 2009
STATUS
approved