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A206831 Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%I A206831 #10 Mar 10 2017 05:27:04
%S A206831 1,1,1,-1,0,1,-1,-3,-1,1,1,0,-4,-2,1,1,5,4,-4,-3,1,-1,0,9,10,-3,-4,1,
%T A206831 -1,-7,-9,9,17,-1,-5,1,1,0,-16,-28,2,24,2,-6,1,1,9,16,-16,-54,-14,30,
%U A206831 6,-7,1,-1,0,25,60,10
%N A206831 Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A206831 Riordan array ((1+x)/(1+x^2), x*(1-x)/(1+x^2)).
%C A206831 Antidiagonal sums are A010892(n).
%H A206831 Indranil Ghosh, <a href="/A206831/b206831.txt">Rows 0..100, flattened</a>
%F A206831 T(n,k) = T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n>1.
%F A206831 G.f.: (1+x)/(1-y*x+(1+y)*x^2).
%F A206831 Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A057077(n), (-1)^n*A078050(n) for x = -1, 0, 1 respectively.
%e A206831 Triangle begins :
%e A206831 1
%e A206831 1, 1
%e A206831 -1, 0, 1
%e A206831 -1, -3, -1, 1
%e A206831 1, 0, -4, -2, 1
%e A206831 1, 5, 4, -4, -3, 1
%e A206831 -1, 0, 9, 10, -3, -4, 1
%e A206831 -1, -7, -9, 9, 17, -1, -5, 1
%e A206831 1, 0, -16, -28, 2, 24, 2, -6, 1
%e A206831 1, 9, 16, -16, -54, -14, 30, 6, -7, 1
%e A206831 -1, 0, 25, 60, 10, -80, -40, 34, 11, -8, 1
%t A206831 nmax=10; Flatten[CoefficientList[Series[CoefficientList[Series[(1 + x)/(1 - y*x + (1 + y)*x^2), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* _Indranil Ghosh_, Mar 10 2017 *)
%Y A206831 Cf. A129267, A007318, A147703, A147721
%Y A206831 Cf. A057077, A087960
%K A206831 easy,sign,tabl
%O A206831 0,8
%A A206831 _Philippe Deléham_, Feb 13 2012