A071014 Binomial transform of A002487.

1, 3, 6, 13, 29, 64, 137, 285, 584, 1197, 2479, 5198, 10989, 23275, 49122, 102951, 213915, 440478, 899177, 1821577, 3668080, 7358199, 14742653, 29582240, 59593613, 120742119, 246254254, 505494077, 1043327165, 2161750892, 4488143133, 9319949375, 19326922734

Offset

1,2

Comments

The transform omits the initial two terms 0, 1 of A002487. - Georg Fischer, Oct 15 2021

Links

Table of n, a(n) for n=1..33.

N. J. A. Sloane, Transforms

Maple

b:= proc(n) option remember; `if`(n<2, n,
      (q-> b(q)+(n-2*q)*b(n-q))(iquo(n, 2)))
    end:
a:= n-> add(b(n+2-j)*binomial(n-1, j-1), j=1..n):
seq(a(n), n=1..33);  # Alois P. Heinz, Oct 15 2021

Mathematica

b[n_] := b[n] = If[n < 2, n,
     With[{q = Quotient[n, 2]}, b[q] + (n-2*q)*b[n-q]]];
a[n_] := Sum[b[n+2-j]*Binomial[n-1, j-1], {j, 1, n}];
Table[a[n], {n, 1, 33}] (* Jean-François Alcover, Apr 25 2022, after Alois P. Heinz *)

Crossrefs

Sequence in context: A002478 A106496 A052933 * A214260 A078061 A018909

Adjacent sequences: A071011 A071012 A071013 * A071015 A071016 A071017

Keyword

nonn

Author

N. J. A. Sloane, May 24 2002

Status

approved