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A210637 Triangle T(n,k), read by rows, given by (2, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%I A210637 #10 Aug 08 2015 10:30:40
%S A210637 1,2,2,5,8,3,12,27,20,5,29,84,91,44,8,70,248,352,251,90,13,169,708,
%T A210637 1240,1164,618,176,21,408,1973,4106,4771,3344,1414,334,34,985,5400,
%U A210637 13010,18000,15645,8748,3073,620,55
%N A210637 Triangle T(n,k), read by rows, given by (2, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A210637 Row sums are powers of 4 (A000302).
%F A210637 G.f.: (1+y*x)/(1-(y+2)*x-(y+1)^2*x^2).
%F A210637 T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k<0 or if k>n.
%F A210637 Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A159612(n+1), (-1)^n*A000034(n), A000007(n), A000129(n+1), A000302(n) for x = -3, -2, -1, 0, 1 respectively.
%F A210637 T(n,0) = A000129(n+1), T(n,n) = A000045(n+2), T(n+1,n) = 2*A004798(n+1).
%e A210637 Triangle begins :
%e A210637 1
%e A210637 2, 2
%e A210637 5, 8, 3
%e A210637 12, 27, 20, 5
%e A210637 29, 84, 91, 44, 8
%e A210637 70, 248, 352, 251, 90, 13
%e A210637 169, 708, 1240, 1164, 618, 176, 21
%e A210637 408, 1973, 4106, 4771, 3344, 1414, 334, 34
%e A210637 985, 5400, 13010, 18000, 15645, 8748, 3073, 620, 55
%e A210637 2378, 14574, 39880, 63966, 66282, 46014, 21400, 6429, 1132, 89
%e A210637 5741, 38896, 119129, 217232, 261185, 216348, 125028, 49772, 13061, 2040, 144
%Y A210637 Cf. A000045, A000129, A000302, A261056 (2nd column).
%K A210637 easy,nonn,tabl
%O A210637 0,2
%A A210637 _Philippe Deléham_, Mar 26 2012