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%I #18 Oct 08 2017 05:55:38
%S 1,1,1,4,5,1,25,33,9,1,172,238,78,13,1,1201,1745,667,139,17,1,8404,
%T 12807,5583,1376,216,21,1,58825,93841,45822,12950,2429,309,25,1,
%U 411772,686288,370108,117458,25366,3890,418,29,1,2882401,5009889,2951034,1035834,251583,44607,5823,543,33,1
%N a(n) = C(3,n) DELTA C(0,n).
%C Triangle [1,3,3,1,0,0,0,...] DELTA [1,0,0,0,...] with Deléham DELTA as in A084938.
%C First column is A034494(n-1). Row sums are A147725. A147724 = A147723*A007318.
%H Indranil Ghosh, <a href="/A147724/b147724.txt">Rows 0..100, flattened</a>
%F Riordan array ((1-7x+3x^2)/(1-8x+7x^2), x(1-4x)/(1-8x+7x^2).
%F G.f.: (1 - 7*x + 3*x^2)/(1 - 8*x + 7*x^2 - x*y + 4*x^2*y). - _Philippe Deléham_ , Oct 29 2013
%F T(n,k) = 8*T(n-1,k) + T(n-1,k-1) - 7*T(n-2,k) - 4*T(n-2,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 4, T(2,1) = 5, T(n,k) = 0 if k > n or if k < 0. - _Philippe Deléham_ , Oct 29 2013
%e Triangle begins
%e 1;
%e 1, 1;
%e 4, 5, 1;
%e 25, 33, 9, 1;
%e 172, 238, 78, 13, 1;
%t nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 7*x + 3*x^2)/(1 - 8*x + 7*x^2 - x*y + 4*x^2*y) , {x, 0, nmax}], x], {y, 0, nmax}], y]] (* _Indranil Ghosh_, Mar 10 2017 *)
%Y Cf. A147721.
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Nov 11 2008
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