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%I A206735 #16 Dec 05 2015 10:02:18
%S A206735 1,0,1,0,2,1,0,3,3,1,0,4,6,4,1,0,5,10,10,5,1,0,6,15,20,15,6,1,0,7,21,
%T A206735 35,35,21,7,1,0,8,28,56,70,56,28,8,1,0,9,36,84,126,126,84,36,9,1,0,10,
%U A206735 45,120,210,252,210,120,45,10,1,0,11,55,165,330,462,462,330,165,55,11,1
%N A206735 Triangle T(n,k), read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A206735 A103452*A007318 as infinite lower triangular matrices.
%C A206735 Essentially the same as A199011.
%F A206735 T(n,k) = A007318(n,k) - A073424(n,k).
%F A206735 Sum_{k, 0<=k<=n} T(n,k)*x^k = (1+x)^n - 1 + 0^n.
%F A206735 T(n,0) = 0^n = A000007(n), T(n,k) = binomial(n,k) for k>0.
%F A206735 G.f.: (1-2*x+(1+y)*x^2)/(1-2x+(1+y)*x^2-y*x).
%F A206735 Sum{k, 0<=k<=n} T(n,k)^x = A000027(n+1), A000225(n), A030662(n), A096191(n), A096192(n) for x = 0, 1, 2, 3, 4 respectively.
%e A206735 Triangle begins :
%e A206735 1
%e A206735 0, 1
%e A206735 0, 2, 1
%e A206735 0, 3, 3, 1
%e A206735 0, 4, 6, 4, 1
%e A206735 0, 5, 10, 10, 5, 1
%e A206735 0, 6, 15, 20, 15, 6, 1
%e A206735 0, 7, 21, 35, 35, 21, 7, 1
%e A206735 0, 8, 28, 56, 70, 56, 28, 8, 1
%e A206735 0, 9, 36, 84, 126, 126, 84, 36, 9, 1
%e A206735 0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1
%e A206735 0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1
%Y A206735 Cf. A007318, A000071 (antidiagonal sums).
%K A206735 easy,nonn,tabl
%O A206735 0,5
%A A206735 _Philippe Deléham_, Feb 11 2012

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