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A238241 Riordan array (1/(1-x-x^2)^2, x/(1-x-x^2)^2).

%I A238241 #10 Apr 29 2015 06:35:54
%S A238241 1,2,1,5,4,1,10,14,6,1,20,40,27,8,1,38,105,98,44,10,1,71,256,315,192,
%T A238241 65,12,1,130,594,924,726,330,90,14,1,235,1324,2534,2472,1430,520,119,
%U A238241 16,1,420,2860,6588,7776,5522,2535,770,152,18,1,744,6020,16407,22968
%N A238241 Riordan array (1/(1-x-x^2)^2, x/(1-x-x^2)^2).
%C A238241 Row sums are A097472(n).
%F A238241 T(n,k) = A037027(n+k+1, 2*k+1).
%F A238241 T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + T(n-2,k) - 2*T(n-3,k) - T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n.
%F A238241 G.f.: -1/(x*y-x^4-2*x^3+x^2+2*x-1). - _Vladimir Kruchinin_, Apr 29 2015
%e A238241 Triangle begins:
%e A238241 1;
%e A238241 2, 1;
%e A238241 5, 4, 1;
%e A238241 10, 14, 6, 1;
%e A238241 20, 40, 27, 8, 1;
%e A238241 38, 105, 98, 44, 10, 1;
%e A238241 71, 256, 315, 192, 65, 12, 1;
%e A238241 130, 594, 924, 726, 330, 90, 14, 1;
%e A238241 ...
%t A238241 T[0, 0] = 1; T[n_, k_] := SeriesCoefficient[-1/(x*y - x^4 - 2*x^3 + x^2 + 2*x - 1), {x, 0, n}, {y, 0, k}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 29 2015, after _Vladimir Kruchinin_ *)
%Y A238241 Cf. A037027, A152440
%Y A238241 Cf. Diagonals: A000012, A005843, A014106
%Y A238241 Cf. Columns: A001629, A001872, A001874
%K A238241 nonn,tabl
%O A238241 0,2
%A A238241 _Philippe Deléham_, Feb 20 2014