%I #10 Nov 02 2023 10:30:19

%S 1,3,8,20,49,119,289,705,1731,4283,10690,26934,68531,176115,457110,

%T 1198128,3170607,8468277,22818167,61999531,169778889,468292663,

%U 1300270333,3632269293,10202425207,28798822159,81652955889,232429744843,663969970203,1902716831527

%N Binomial transform of A000029.

%H Alois P. Heinz, <a href="/A054192/b054192.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ 3^(n+1) / (4*n). - _Vaclav Kotesovec_, Nov 02 2023

%p with(numtheory):

%p b:= proc(n) option remember; ceil(add(

%p phi(d)*2^(n/d)/(2*n), d=divisors(n))+

%p `if`(n::odd, 2^((n-1)/2), 2^(n/2-1)+2^(n/2-2)))

%p end:

%p a:= n-> add(b(n-j)*binomial(n, j), j=0..n):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Jul 17 2017

%t 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 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 29 2000