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%I #20 Oct 08 2017 05:55:33
%S 1,1,1,3,4,1,11,17,7,1,41,72,40,10,1,153,301,208,72,13,1,571,1244,
%T 1021,446,113,16,1,2131,5093,4819,2525,813,163,19,1,7953,20688,22104,
%U 13452,5218,1336,222,22,1,29681,83481,99192,68568,30986,9586,2042,290,25,1
%N a(n) = C(2,n) DELTA C(0,n).
%C Triangle T equal to [1,2,1,0,0,0,...] DELTA [1,0,0,0,...] for Deléham DELTA as in A084938.
%C T = A147720*A007318. Row sums are A147722.
%H Indranil Ghosh, <a href="/A147721/b147721.txt">Rows 0..100, flattened</a>
%F Riordan array ((1-3x)/(1-4x+x^2), x(1-x)/(1-4x+x^2)).
%F T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n > 1. - _Philippe Deléham_, Feb 13 2012
%F G.f.: (1-3*x)/(1-4*x+(1+y)*x^2-y*x). - _Philippe Deléham_, Feb 13 2012
%F Sum_{k=0..n} T(n,k)*x^k = A000007(n), A001835(n), A147722(n), A084120(n) for x = -1, 0, 1, 2 respectively. - _Philippe Deléham_, Feb 13 2012
%e Triangle begins
%e 1;
%e 1, 1;
%e 3, 4, 1;
%e 11, 17, 7, 1;
%e 41, 72, 40, 10, 1;
%e 153, 301, 208, 72, 13, 1;
%t nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 3*x)/(1 - 4*x + (1 + y)*x^2 - y*x), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* _Indranil Ghosh_, Mar 10 2017, after _Philippe Deléham_ *)
%Y Cf. A129267, A007318, A147703.
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Nov 11 2008
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