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

Author

N. J. A. Sloane, Jun 10 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..50
• N. J. A. Sloane, Transforms

Programs

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 *)