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

0,3

Links

Table of n, a(n) for n=0..59.

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.

Formula

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

Example

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;
  ...

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A318683 A028364 A239482 * A011971 A060048 A110699

Adjacent sequences: A280467 A280468 A280469 * A280471 A280472 A280473

Keyword

nonn,tabl

Author

Tony Foster III, Jan 03 2017

Status

approved