A280470 Triangle A106534 with reversed rows.

1, 1, 2, 2, 3, 5, 5, 7, 10, 15, 14, 19, 26, 36, 51, 42, 56, 75, 101, 137, 188, 132, 174, 230, 305, 406, 543, 731, 429, 561, 735, 965, 1270, 1676, 2219, 2950, 1430, 1859, 2420, 3155, 4120, 5390, 7066, 9285, 12235, 4862, 6292, 8151, 10571, 13726, 17846, 23236, 30302, 39587, 51822, 16796, 21658, 27950, 36101, 46672

Offset: 0

Author

Tony Foster III, Jan 03 2017

Keywords

• nonn
• tabl

Examples

			Fibonacci Determinant Triangle:
    1;
    1,    2;
    2,    3,    5;
    5,    7,   10,   15;
   14,   19,   26,   36,   51;
   42,   56,   75,  101,  137,  188;
  132,  174,  230,  305,  406,  543,  731;
  429,  561,  735,  965, 1270, 1676, 2219, 2950;
  ...
		

Links

• P. Barry, A. Hennessy, The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences, J. Int. Seq. 13 (2010) # 10.8.2, page 5
• A. Cvetkovi, Predrag Rajkovic, and Milos IvkoviCatalan Numbers, the Hankel Transform, and Fibonacci Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.3.

Crossrefs

Cf. A000108, A001519, A007317, A011971, A103433, A106534, A197649.

Programs

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

Mathematica

Table[Sum[Binomial[k, j] CatalanNumber[n - j], {j, 0, k}], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Mar 08 2017 *)

PARI

C(n)=binomial(2*n,n)/(n+1);
T(n,k)=sum(j=0,k,binomial(k,j)*C(n-j));
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print()); \\ Joerg Arndt, Jan 15 2017

Formula

T(n,k) = Sum_{j=0..k} binomial(k,j) * A000108(n-j). - Joerg Arndt, Jan 15 2017