login
Triangle read by rows, for n > 0, n zeros followed by n.
3

%I #25 Sep 01 2024 14:13:05

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

%T 0,7,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,10,0,0,

%U 0,0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,13

%N Triangle read by rows, for n > 0, n zeros followed by n.

%C Multiplied by the vector [1, 2, 3, ...] from the right gives (1, 2, 6, 12, 20, 30, 42, ...), A002378.

%C Triangle T(n,k), read by rows, given by [0,0,0,0,0,0,0,...] DELTA [1,1,-1,1,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Oct 26 2007

%F Triangle read by rows, a(0) = 1, then for n > 0, n zeros followed by n. Infinite lower triangular matrix with (1, 1, 2, 3, 4, ...) in the main diagonal and the rest zeros.

%F G.f.: (1-x*y+x^2*y^2)/(-1+x*y)^2. - _R. J. Mathar_, Aug 11 2015

%e First few rows of the triangle:

%e 1;

%e 0, 1;

%e 0, 0, 2;

%e 0, 0, 0, 3;

%e 0, 0, 0, 0, 4;

%e 0, 0, 0, 0, 0, 5;

%e ...

%t Join[{1},Flatten[Table[PadLeft[{n},n+1,0],{n,15}]]] (* _Harvey P. Dale_, May 08 2012 *)

%Y Cf. A134403, A005449.

%Y Essentially the same as A130460.

%K nonn,easy,tabl

%O 0,6

%A _Gary W. Adamson_, Oct 23 2007