A071897 CONTINUANT transform of Catalan numbers 1, 2, 5, 14, 42, ...

1, 3, 16, 227, 9550, 1260827, 540904333, 773494457017, 3760730590920987, 63165231778603354669, 3713231319097707398492821, 772396673211317543153892036521, 573813488532401034128124101329943721, 1534629746271367018386831539104008577227761

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..50

N. J. A. Sloane, Transforms

Maple

a:= proc(n) option remember; `if`(n<0, 0,
      `if`(n=0, 1, binomial(2*n, n)/(n+1) *a(n-1) +a(n-2)))
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 06 2013

Mathematica

a[n_] := a[n] = If[n<0, 0, If[n==0, 1, CatalanNumber[n]*a[n-1] + a[n-2]]]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)

Crossrefs

Sequence in context: A113597 A361366 A000273 * A182012 A272385 A013923

Adjacent sequences: A071894 A071895 A071896 * A071898 A071899 A071900

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2002

Status

approved