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A280470 Triangle A106534 with reversed rows.

%I A280470 #38 Sep 08 2022 08:46:18
%S A280470 1,1,2,2,3,5,5,7,10,15,14,19,26,36,51,42,56,75,101,137,188,132,174,
%T A280470 230,305,406,543,731,429,561,735,965,1270,1676,2219,2950,1430,1859,
%U A280470 2420,3155,4120,5390,7066,9285,12235,4862,6292,8151,10571,13726,17846,23236,30302,39587,51822,16796,21658,27950,36101,46672
%N A280470 Triangle A106534 with reversed rows.
%H A280470 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 A280470 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 A280470 T(n,k) = Sum_{j=0..k} binomial(k,j) * A000108(n-j). - _Joerg Arndt_, Jan 15 2017
%e A280470 Fibonacci Determinant Triangle:
%e A280470     1;
%e A280470     1,    2;
%e A280470     2,    3,    5;
%e A280470     5,    7,   10,   15;
%e A280470    14,   19,   26,   36,   51;
%e A280470    42,   56,   75,  101,  137,  188;
%e A280470   132,  174,  230,  305,  406,  543,  731;
%e A280470   429,  561,  735,  965, 1270, 1676, 2219, 2950;
%e A280470   ...
%t A280470 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 A280470 (PARI) C(n)=binomial(2*n,n)/(n+1);
%o A280470 T(n,k)=sum(j=0,k,binomial(k,j)*C(n-j));
%o A280470 for(n=0,10,for(k=0,n,print1(T(n,k),", "));print()); \\ _Joerg Arndt_, Jan 15 2017
%o A280470 (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 A280470 Cf. A000108, A001519, A007317, A011971, A103433, A106534, A197649.
%K A280470 nonn,tabl
%O A280470 0,3
%A A280470 _Tony Foster III_, Jan 03 2017