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A152440 Riordan matrix (1/(1-x-x^2),x/(1-x-x^2)^2).

%I A152440 #10 Feb 21 2014 03:56:10
%S A152440 1,1,1,2,3,1,3,9,5,1,5,22,20,7,1,8,51,65,35,9,1,13,111,190,140,54,11,
%T A152440 1,21,233,511,490,255,77,13,1,34,474,1295,1554,1035,418,104,15,1,55,
%U A152440 942,3130,4578,3762,1925,637,135,17,1,89,1836,7285,12720,12573,7865,3276
%N A152440 Riordan matrix (1/(1-x-x^2),x/(1-x-x^2)^2).
%C A152440 From _Philippe Deléham_, Feb 20 2014: (Start)
%C A152440 T(n,0)   = A000045(n+1);
%C A152440 T(n+1,1) = A001628(n);
%C A152440 T(n+2,2) = A001873(n);
%C A152440 T(n+3,3) = A001875(n).
%C A152440 Row sums are A238236(n). (End)
%F A152440 a(n,k) = sum( binomial(n-j-k,2k) binomial(n-j-k,j), j=0...(n-k)/2 )
%F A152440 a(n,k) = sum( binomial(i+2k,2k) binomial(n-i+k,i+2k), i=0...(n - k)/2 )
%F A152440 Recurrence: a(n+4,k+1) - 2 a(n+3,k+1) - a(n+3,k) - a(n+2,k+1) + 2 a(n+1,k+1) + a(n,k+1) = 0
%F A152440 GF for columns: 1/(1-x-x^2)(x/(1-x-x^2)^2)^k
%F A152440 GF: (1-x-x^2)/((1-x-x^2)^2-xy)
%F A152440 T(n,k) = A037027(n+k, 2*k). - _Philippe Deléham_, Feb 20 2014
%e A152440 Triangle begins:
%e A152440 1;
%e A152440 1, 1;
%e A152440 2, 3, 1;
%e A152440 3, 9, 5, 1;
%e A152440 5, 22, 20, 7, 1;
%e A152440 8, 51, 65, 35, 9, 1;
%e A152440 13, 111, 190, 140, 54, 11, 1;
%e A152440 21, 233, 511, 490, 255, 77, 13, 1, etc.
%e A152440 - _Philippe Deléham_, Feb 20 2014
%Y A152440 The first row is given by A000045.
%Y A152440 Cf. A037027, A238241.
%K A152440 nonn,tabl,easy
%O A152440 0,4
%A A152440 _Emanuele Munarini_, Dec 04 2008, Dec 05 2008