A128132 - OEIS

%I #22 Jul 27 2020 04:58:55

%S 1,-1,2,0,-1,3,0,0,-1,4,0,0,0,-1,5,0,0,0,0,-1,6,0,0,0,0,0,-1,7,0,0,0,

%T 0,0,0,-1,8,0,0,0,0,0,0,0,-1,9,0,0,0,0,0,0,0,0,-1,10,0,0,0,0,0,0,0,0,

%U 0,-1,11,0,0,0,0,0,0,0,0,0,0,-1,12

%N A natural number transform, companion to A127701.

%C Binomial transform is A128133.

%F T(n,n) = n.

%F T(n,n-1) = -1.

%F T(n,k) = 0 for k <> n, n-1.

%e Triangle T(n,k) (with rows n >= 1 and columns k = 1..n) begins:

%e    1;

%e   -1,  2;

%e    0, -1,  3;

%e    0,  0, -1,  4;

%e    0,  0,  0, -1,  5;

%e    0,  0,  0,  0, -1, 6;

%e    ...

%p A128132 := proc(n,k)

%p     if n = k then

%p         n;

%p     elif k = n-1 then

%p         -1 ;

%p     else

%p         0 ;

%p     end if;

%p end proc: # _R. J. Mathar_, Apr 26 2016

%t {1}~Join~Table[PadLeft[{-1, n}, n], {n, 2, 12}] // Flatten (* _Michael De Vlieger_, Apr 26 2016 *)

%Y Cf. A127701, A128133, A128134.

%K tabl,sign,easy

%O 1,3

%A _Gary W. Adamson_, Feb 15 2007