This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A183189 #13 Oct 16 2024 06:02:43
%S A183189 1,2,0,6,1,0,18,5,0,0,54,21,1,0,0,162,81,8,0,0,0,486,297,45,1,0,0,0,
%T A183189 1458,1053,216,11,0,0,0,0,4374,3645,945,78,1,0,0,0,0,13122,12393,3888,
%U A183189 450,14,0,0,0,0,0
%N A183189 Triangle T(n,k), read by rows, given by (2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A183189 Riordan array ((1-x)/(1-3x), x^2/(1-3x)).
%C A183189 A skewed version of triangular array in A193723.
%C A183189 A202209*A007318 as infinite lower triangular matrices.
%F A183189 G.f.: (1-x)/(1-3*x-y*x^2).
%F A183189 T(n,k) = Sum_{j, j>=0} T(n-2-j,k-1)*3^j.
%F A183189 T(n,k) = 3*T(n-1,k) + T(n-2,k-1).
%F A183189 Sum_{k, 0<=k<=n} T(n,k)*x^k = A057682(n+1), A000079(n), A122367(n), A025192(n), A052924(n), A104934(n), A202206(n), A122117(n), A197189(n) for x = -3, -2, -1, 0, 1, 2, 3, 4, 5 respectively.
%e A183189 Triangle begins:
%e A183189 1
%e A183189 2, 0
%e A183189 6, 1, 0
%e A183189 18, 5, 0, 0
%e A183189 54, 21, 1, 0, 0
%e A183189 162, 81, 8, 0, 0, 0
%e A183189 486, 297, 45, 1, 0, 0, 0
%Y A183189 Cf. A000244, A025192, A081038, A183188 (antidiagonal sums).
%K A183189 nonn,tabl
%O A183189 0,2
%A A183189 _Philippe Deléham_, Dec 14 2011