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%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
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