A206831 - OEIS

%I #10 Mar 10 2017 05:27:04

%S 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 -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 6,-7,1,-1,0,25,60,10

%N 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 Riordan array ((1+x)/(1+x^2), x*(1-x)/(1+x^2)).

%C Antidiagonal sums are A010892(n).

%H Indranil Ghosh, <a href="/A206831/b206831.txt">Rows 0..100, flattened</a>

%F T(n,k) = T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n>1.

%F G.f.: (1+x)/(1-y*x+(1+y)*x^2).

%F 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 Triangle begins :

%e 1

%e 1, 1

%e -1, 0, 1

%e -1, -3, -1, 1

%e 1, 0, -4, -2, 1

%e 1, 5, 4, -4, -3, 1

%e -1, 0, 9, 10, -3, -4, 1

%e -1, -7, -9, 9, 17, -1, -5, 1

%e 1, 0, -16, -28, 2, 24, 2, -6, 1

%e 1, 9, 16, -16, -54, -14, 30, 6, -7, 1

%e -1, 0, 25, 60, 10, -80, -40, 34, 11, -8, 1

%t 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 Cf. A129267, A007318, A147703, A147721

%Y Cf. A057077, A087960

%K easy,sign,tabl

%O 0,8

%A _Philippe Deléham_, Feb 13 2012