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A129186 Right shift operator generating 1's in shifted spaces.

%I A129186 #20 May 18 2020 20:15:28
%S A129186 1,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
%T A129186 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U A129186 0,0,0,0,0,0,0,0
%N A129186 Right shift operator generating 1's in shifted spaces.
%C A129186 Let A129186 = M, then M*V, V a vector; shifts V to the right, appending 1's to the shifted spaces. Example: M*V, V = [1,2,3,...] = [1,1,2,3,...].
%C A129186 Triangle T(n,k), read by rows, given by (1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 08 2011
%H A129186 Robert Price, <a href="/A129186/b129186.txt">Table of n, a(n) for n = 0..5049</a>
%F A129186 Infinite lower triangular matrix with (1,0,0,...) in the main diagonal and (1,1,1...) in the subdiagonal.
%F A129186 G.f.: (1-(y-1)*x)/(1-y*x). - _Philippe Deléham_, Dec 08 2011
%e A129186 First few rows of the triangle are:
%e A129186 1;
%e A129186 1, 0;
%e A129186 0, 1, 0;
%e A129186 0, 0, 1, 0;
%e A129186 0, 0, 0, 1, 0;
%e A129186 ...
%p A129186 gf := 1 + z/(1 - x*z): ser := series(gf, z, 16): c := k -> coeff(ser, z, k):
%p A129186 seq(seq(coeff(c(n), x, k), k=0..n), n=0..14); # _Peter Luschny_, Jul 07 2019
%t A129186 Join[{1},Flatten[Table[PadLeft[{1,0},n,0],{n,2,20}]]] (* _Harvey P. Dale_, Aug 26 2019 *)
%Y A129186 Generalized Eulerian triangles: this sequence (m=0), A173018 (m=1), A292604 (m=2).
%Y A129186 Cf. A000012 (row sums), A071919, A129184, A129185.
%K A129186 nonn,easy,tabl
%O A129186 0,1
%A A129186 _Gary W. Adamson_, Apr 01 2007