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%I #24 Feb 07 2020 06:15:12
%S 1,0,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,
%T 1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,
%U 1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Triangle T(n,k), 0 <= k <= n, read by rows given by [0,1,0,0,0,0,0,0,0,0,...] DELTA [1,0,-1,1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
%C Diagonal sums give A123108. - _Philippe Deléham_, Oct 08 2009
%F Sum_{k=0..n} T(n,k)*x^k = A000007(n), A028310(n), A095121(n), A123109(n) for x=0,1,2,3 respectively.
%F G.f.: (1-x+y*x^2)/(1-(1+y)*x+y*x^2). - _Philippe Deléham_, Nov 01 2011
%F From _Tom Copeland_, Nov 10 2012: (Start)
%F O.g.f. for row polynomials: 1 + (t/(1-t))*(1/(1-x)-1/(1-x*t)) = 1 + t*x + (t+t^2)*x^2 + ....
%F E.g.f. for row polynomials: 1 + (t/(1-t))*(e^x-e^(t*x)) = 1 + t*x + (t+t^2)*x^2/2 + .... (End)
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 1, 1;
%e 0, 1, 1, 1;
%e 0, 1, 1, 1, 1;
%e 0, 1, 1, 1, 1, 1;
%e 0, 1, 1, 1, 1, 1, 1;
%e 0, 1, 1, 1, 1, 1, 1, 1;
%e 0, 1, 1, 1, 1, 1, 1, 1, 1;
%e 0, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%Y Essentially the same sequence as A114607.
%Y Also essentially the same as A023532. - _R. J. Mathar_, Jun 18 2008
%K nonn,tabl
%O 0,1
%A _Philippe Deléham_, Sep 28 2006
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