cp's OEIS Frontend

A166124 Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

%I A166124 #8 Nov 09 2013 14:16:09
%S A166124 1,0,2,0,1,2,0,1,1,2,0,1,1,1,2,0,1,1,1,1,2,0,1,1,1,1,1,2,0,1,1,1,1,1,
%T A166124 1,2,0,1,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,1,2,0,1,
%U A166124 1,1,1,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,1,1,1,1,2
%N A166124 Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
%F A166124 Sum_{k, 0<=k<=n} T(n,k)*x^(n-k)= A166122(n), A166114(n), A084222(n), A084247(n), A000034(n), A040000(n), A000027(n+1), A000079(n), A007051(n), A047849(n), A047850(n), A047851(n), A047852(n), A047853(n), A047854(n), A047855(n), A047856(n) for x= -5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11 respectively.
%F A166124 Sum_{k, 0<=k<=n} T(n,k)*x^k= A000007(n), A000027(n+1), A033484(n), A134931(n), A083597(n) for x= 0,1,2,3,4 respectively.
%F A166124 T(n,k)= A166065(n,k)/2^(n-k).
%F A166124 G.f.: (1-x+x*y)/(1-x-x*y+x^2*y). - _Philippe Deléham_, Nov 09 2013
%F A166124 T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Nov 09 2013
%e A166124 Triangle begins :
%e A166124 1 ;
%e A166124 0,2 ;
%e A166124 0,1,2 ;
%e A166124 0,1,1,2 ;
%e A166124 0,1,1,1,2 ;
%e A166124 0,1,1,1,1,2 ;
%e A166124 0,1,1,1,1,1,2 ; ...
%K A166124 nonn,tabl
%O A166124 0,3
%A A166124 _Philippe Deléham_, Oct 07 2009