A159881 - OEIS

%I #13 Jul 27 2018 20:36:30

%S 1,2,-1,3,-3,1,4,-6,5,-1,5,-10,16,-8,1,6,-15,42,-40,12,-1,7,-21,99,

%T -162,88,-17,1,8,-28,219,-585,514,-173,23,-1,9,-36,466,-1974,2641,

%U -1379,311,-30,1,10,-45,968,-6388,12538,-9536,3245,-521,38,-1

%N 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).

%H G. C. Greubel, <a href="/A159881/b159881.txt">Rows n=0..100 of triangle, flattened</a>

%F Conjecture row sums: Sum_{k=0..n} |T(n,k)| = A029761(n). - _R. J. Mathar_, May 29 2009

%e Triangle begins :

%e 1;

%e 2, -1;

%e 3, -3, 1;

%e 4, -6, 5, -1;

%e 5, -10, 16, -8, 1;

%e 6, -15, 42, -40, 12, -1;

%e 7, -21, 99, -162, 88, -17, 1;

%e 8, -28, 219, -585, 514, -173, 23, -1;

%e 9, -36, 466, -1974, 2641, -1379, 311, -30, 1;

%e 10, -45, 968, -6388, 12538, -9536, 3245, -521, 38, -1;

%e 11, -55, 1981, -20132, 56540, -60218, 29006, -6892, 825, -47, 1;

%p 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

%t 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 *)

%o (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)))};

%o for(n=0,15, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Jul 27 2018

%Y Cf. A000027, A000217, A002662, A152948

%K easy,sign,tabl

%O 0,2

%A _Philippe Deléham_, Apr 25 2009