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%I #16 Oct 08 2017 05:55:25
%S 1,0,1,0,2,1,0,6,4,1,0,18,16,6,1,0,54,60,30,8,1,0,162,216,134,48,10,1,
%T 0,486,756,558,248,70,12,1,0,1458,2592,2214,1168,410,96,14,1,0,4374,
%U 8748,8478,5160,2150,628,126,16
%N Riordan array (1, x(1-x)/(1-3x)).
%C Array [0,2,1,0,0,0,....] DELTA [1,0,0,0,......] for Deléham DELTA as in A084938.
%C Row sums are A001835. Diagonal sums are related to A030186.
%C Row sums of inverse are essentially A091593. A147720*A007318 is A147721.
%H Indranil Ghosh, <a href="/A147720/b147720.txt">Rows 0..100, flattened</a>
%F Sum_{k=0..n} T(n,k)*x^k = A000007(n), A001835(n), A147722(n), A084120(n) for x = 0, 1, 2, 3 respectively. - _Philippe Deléham_, Nov 15 2008
%F G.f.: (1-3*x)/(1-(3+y)*x+y*x^2). - _Philippe Deléham_, Feb 15 2012
%e Triangle begins
%e 1;
%e 0, 1;
%e 0, 2, 1;
%e 0, 6, 4, 1;
%e 0, 18, 16, 6, 1;
%e 0, 54, 60, 30, 8, 1;
%e 0, 162, 216, 134, 48, 10, 1;
%t nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1-3*x)/(1-(3+y)*x+y*x^2), {x, 0, nmax}],x],{y,0,nmax}],y]] (* _Indranil Ghosh_, Mar 10 2017, after _Philippe Deléham_ *)
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Nov 11 2008