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%I #10 Jan 28 2018 02:46:05
%S 1,1,1,2,2,2,6,3,3,6,18,4,4,8,18,52,5,5,10,24,52,148,6,6,12,30,70,148,
%T 420,7,7,14,36,88,200,420,1192,8,8,16,42,106,252,568,1192,3384,9,9,18,
%U 48,124,304,716,1612,3384,9608,10,10,20,54,142,356,864,2032,4576,9608
%N Choulet-Curtz triangle with T(0,0)=1, T(n,n)=T(n,0).
%C Row sums are in A078484.
%C This sequence is an example of a sequence u(n) which satisfies (using the notation from the link): T_{1,1}(u(0), u(1), u(2), u(3), ...) = (u(1), u(2), u(3), ...). The o.g.f of all such sequences is given by the formula Phi(z)=u(0)*((1-3*z+2*z^2-z^3)/(1-4*z+4*z^2-2*z^3))+((z+z^3)/(1-4*z+4*z^2-2*z^3)) with u(0) in N or Z; the sequences are given by u(n) = u(0)*(1, 1, 2, 5, 14, 40, 114, 324, 920, ...) + (0, 1, 4, 13, 38, 108, 868, 2464, 6996, ...), i.e., u(n) = u(0)*A159035(n) + A159036(n). - _Richard Choulet_, Apr 03 2009
%H Richard Choulet, <a href="http://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%F T(n,k) = T(n-1,k) + T(k-1,k-1), k >= 1, n > k;
%F T(n,n) = T(n,0) = Sum_{k=0..n} T(n-1,k); T(0,0)=1.
%e Triangle begins
%e 1;
%e 1, 1;
%e 2, 2, 2;
%e 6, 3, 3, 6;
%e 18, 4, 4, 8, 18;
%e 52, 5, 5, 10, 24, 52;
%e 148, 6, 6, 12, 30, 70, 148;
%Y Cf. A078484.
%Y Cf. A159035, A159036. - _Richard Choulet_, Apr 03 2009
%K nonn,tabl
%O 0,4
%A _Philippe Deléham_, Mar 20 2009
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