A071896 CONTINUANT transform of triangular numbers 1, 3, 6, 10, ...

1, 4, 25, 254, 3835, 80789, 2265927, 81654161, 3676703172, 202300328621, 13355498392158, 1041931174916945, 94829092415834153, 9958096634837503010, 1195066425272916195353, 162538991933751440071018, 24869660832289243247061107

Offset: 1

Author

N. J. A. Sloane, Jun 10 2002

Keywords

• nonn

Comments

Equals the eigensequence of an infinite lower triangular matrix with (1, 3, 6, ...) in the main diagonal and (1, 1, 1, ...) in the subdiagonal; with the rest zeros. - Gary W. Adamson, Apr 13 2009

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200
• N. J. A. Sloane, Transforms

Programs

Maple

a:= proc(n) option remember; `if`(n<0, 0,
      `if`(n=0, 1, n*(n+1)/2 *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, n*(n+1)/2*a[n-1] + a[n-2]]];
Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *)