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A280470 Triangle A106534 with reversed rows. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A008507 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

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Last modified February 19 02:06 EST 2018. Contains 299330 sequences. (Running on oeis4.)