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%I #10 Sep 08 2013 19:59:10
%S 1,0,1,0,1,1,0,2,2,1,0,2,5,3,1,0,3,8,9,4,1,0,3,14,19,14,5,1,0,4,20,39,
%T 36,20,6,1,0,4,30,69,85,60,27,7,1,0,5,40,119,176,160,92,35,8,1,0,5,55,
%U 189,344,376,273,133,44,9
%N Convolution triangle A059594 with extra first column.
%C Riordan array (1, x/((1+x)*(1-x)^2)). - _Philippe Deléham_, Feb 24 2012
%C Triangle, read by rows, given by (0, 1, 1, -2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Feb 24 2012
%F G.f.for column m >= 0: (x/((1-x^2)*(1-x)))^m.
%F T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k) - T(n-3,k) with T(n,0) = 0^n. - _Philippe Deléham_, Feb 24 2012
%F G.f.: (1-x-x^2+x^3)/(1-x-x^2+x^3-y*x). - _Philippe Deléham_, Feb 24 2012
%F Sum_{k, 0<=k<=n} T(n,k)*2^k = A181301(n). - _Philippe Deléham_, Feb 24 2012
%e {1}; {0,1}; {0,1,1}; {0,2,2,1}; ...
%e Triangle begins :
%e 1
%e 0, 1
%e 0, 1, 1
%e 0, 2, 2, 1
%e 0, 2, 5, 3, 1
%e 0, 3, 8, 9, 4, 1
%e 0, 3, 14, 19, 14, 5, 1
%t t[0, 0] = 1; t[_, 0] = 0; t[n_, m_] := Sum[ Sum[ Binomial[j, 2*j-3*k-m+n]*(-1)^(j-k)*Binomial[k, j], {j, 0, k}]*Binomial[m+k-1, m-1], {k, 0, n-m}]; Table[t[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 21 2013 *)
%Y Cf. A059594,
%K nonn,easy,tabl
%O 0,8
%A _Wolfdieter Lang_, Apr 06 2001
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