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%I A202064 #17 Sep 08 2013 19:59:29
%S A202064 1,2,0,3,1,0,4,4,0,0,5,10,1,0,0,6,20,6,0,0,0,7,35,21,1,0,0,0,8,56,56,
%T A202064 8,0,0,0,0,9,84,126,36,1,0,0,0,0,10,120,252,120,10,0,0,0,0,0,11,165,
%U A202064 462,330,55,1,0,0,0,0,0
%N A202064 Triangle T(n,k), read by rows, given by (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A202064 Riordan array (x/(1-x)^2, x^2/(1-x)^2).
%C A202064 Mirror image of triangle in A119900.
%C A202064 A203322*A130595 as infinite lower triangular matrices. - _Philippe Deléham_, Jan 05 2011
%F A202064 G.f.: 1/((1-x)^2-y*x^2).
%F A202064 Sum_{k, 0<=k<=n} T(n,k)*x^k = A000027(n+1), A000079(n), A000129(n+1), A002605(n+1), A015518(n+1), A063727(n), A002532(n+1), A083099(n+1), A015519(n+1), A003683(n+1), A002534(n+1), A083102(n), A015520(n+1), A091914(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 10, 11, 12, 13 respectively.
%F A202064 T(n,k) = binomial(n+1,2k+1).
%F A202064 T(n,k) = 2*T(n-1,k) + T(n-2,k-1) - T(n-2,k), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0 and T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Mar 15 2012
%e A202064 Triangle begins :
%e A202064 1
%e A202064 2, 0
%e A202064 3, 1, 0
%e A202064 4, 4, 0, 0
%e A202064 5, 10, 1, 0, 0
%e A202064 6, 20, 6, 0, 0, 0
%e A202064 7, 35, 21, 1, 0, 0, 0
%e A202064 8, 56, 56, 8, 0, 0, 0, 0
%Y A202064 Cf. A007318, A000079 (row sums), A005314 (antidiagonal sums), A119900, A034867, A084938, A130595, A203322.
%K A202064 nonn,tabl
%O A202064 0,2
%A A202064 _Philippe Deléham_, Dec 10 2011

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