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%I #38 Sep 08 2022 08:46:18
%S 1,1,2,2,3,5,5,7,10,15,14,19,26,36,51,42,56,75,101,137,188,132,174,
%T 230,305,406,543,731,429,561,735,965,1270,1676,2219,2950,1430,1859,
%U 2420,3155,4120,5390,7066,9285,12235,4862,6292,8151,10571,13726,17846,23236,30302,39587,51822,16796,21658,27950,36101,46672
%N Triangle A106534 with reversed rows.
%H P. Barry, A. Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Barry2/barry94r.html">The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences</a>, J. Int. Seq. 13 (2010) # 10.8.2, page 5
%H A. Cvetkovi, Predrag Rajkovic, and Milos Ivkovi<a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Ivkovic/ivkovic3.html">Catalan Numbers, the Hankel Transform, and Fibonacci Numbers</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.3.
%F T(n,k) = Sum_{j=0..k} binomial(k,j) * A000108(n-j). - _Joerg Arndt_, Jan 15 2017
%e Fibonacci Determinant Triangle:
%e 1;
%e 1, 2;
%e 2, 3, 5;
%e 5, 7, 10, 15;
%e 14, 19, 26, 36, 51;
%e 42, 56, 75, 101, 137, 188;
%e 132, 174, 230, 305, 406, 543, 731;
%e 429, 561, 735, 965, 1270, 1676, 2219, 2950;
%e ...
%t Table[Sum[Binomial[k, j] CatalanNumber[n - j], {j, 0, k}], {n, 0, 10}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Mar 08 2017 *)
%o (PARI) C(n)=binomial(2*n,n)/(n+1);
%o T(n,k)=sum(j=0,k,binomial(k,j)*C(n-j));
%o for(n=0,10,for(k=0,n,print1(T(n,k),", "));print()); \\ _Joerg Arndt_, Jan 15 2017
%o (Magma) &cat [[&+[Binomial(k,j)*Catalan(n-j): j in [0..k]]: k in [0..n]]: n in [0..10]]; // _Bruno Berselli_, Mar 07 2017
%Y Cf. A000108, A001519, A007317, A011971, A103433, A106534, A197649.
%K nonn,tabl
%O 0,3
%A _Tony Foster III_, Jan 03 2017
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