cp's OEIS Frontend

A199011 Triangle T(n,k), read by rows, given by (1,1,-1,1,0,0,0,0,0,0,0,...) DELTA (0,1,0,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

%I A199011 #9 Feb 13 2014 02:34:17
%S A199011 1,1,0,2,1,0,3,3,1,0,4,6,4,1,0,5,10,10,5,1,0,6,15,20,15,6,1,0,7,21,35,
%T A199011 35,21,7,1,0,8,28,56,70,56,28,8,1,0,9,36,84,126,126,84,36,9,1,0,10,45,
%U A199011 120,210,252,210,120,45,10,1,0
%N A199011 Triangle T(n,k), read by rows, given by (1,1,-1,1,0,0,0,0,0,0,0,...) DELTA (0,1,0,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
%C A199011 Mirror image of triangle in A198321.
%C A199011 Variant of A074909, A135278.
%F A199011 T(n,k)=binomial(n,k+1).
%F A199011 Sum_{0<=k<=n} T(n,k)*x^k = ((x+1)^n-1)/x for n>0.
%F A199011 G.f.: (1-(1+y)*x+(1+y)*x^2)/(1-(2+y)*x+(1+y)*x^2).
%F A199011 T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0, T(2,0) = 2, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Feb 12 2014
%e A199011 Triangle begins :
%e A199011 1
%e A199011 1, 0
%e A199011 2, 1, 0
%e A199011 3, 3, 1, 0
%e A199011 4, 6, 4, 1, 0
%e A199011 5, 10, 10, 5, 1, 0
%e A199011 6, 15, 20, 15, 6, 1, 0
%Y A199011 Cf. A007318, A074909, A135278, A198321
%K A199011 easy,nonn,tabl
%O A199011 0,4
%A A199011 _Philippe Deléham_, Nov 01 2011