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A054192 Binomial transform of A000029. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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-Fran├žois 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

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Last modified May 24 17:39 EDT 2019. Contains 323534 sequences. (Running on oeis4.)