A054192 Binomial transform of A000029.

1, 3, 8, 20, 49, 119, 289, 705, 1731, 4283, 10690, 26934, 68531, 176115, 457110, 1198128, 3170607, 8468277, 22818167, 61999531, 169778889, 468292663, 1300270333, 3632269293, 10202425207, 28798822159, 81652955889, 232429744843, 663969970203, 1902716831527

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 3^(n+1) / (4*n). - Vaclav Kotesovec, Nov 02 2023

Maple

with(numtheory):
b:= proc(n) option remember; ceil(add(
      phi(d)*2^(n/d)/(2*n), d=divisors(n))+
     `if`(n::odd, 2^((n-1)/2), 2^(n/2-1)+2^(n/2-2)))
    end:
a:= n-> add(b(n-j)*binomial(n, j), j=0..n):
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 17 2017

Mathematica

a29[n_] := If[n == 0, 1, DivisorSum[n, EulerPhi[#]*2^(n/#)&]/(2*n) + If[OddQ[n], 2^((n-1)/2), 2^(n/2-1) + 2^(n/2-2)]]; a[n_] := Sum[Binomial[n, k] * a29[k], {k, 0, n}]; Array[a, 28, 0] (* Jean-François Alcover, Jul 17 2017 *)

Crossrefs

Sequence in context: A126876 A090757 A048739 * A124523 A054185 A171853

Adjacent sequences: A054189 A054190 A054191 * A054193 A054194 A054195

Keyword

nonn

Author

N. J. A. Sloane, Apr 29 2000

Status

approved