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

1,2

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

Formula

a(n) ~ c * n!^2 * n / 2^n, where c = 1.43178672478173431270398655351152085810634769818312187015889240083... - Vaclav Kotesovec, Feb 11 2026

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 *)

Crossrefs

Sequence in context: A220356 A210809 A380029 * A065740 A376160 A308008

Adjacent sequences: A071893 A071894 A071895 * A071897 A071898 A071899

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2002

Status

approved