The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A054192

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A054192

Binomial transform of A000029.
(history; published version)

#10 by Vaclav Kotesovec at Thu Nov 02 10:30:19 EDT 2023

STATUS

editing

approved

#9 by Vaclav Kotesovec at Thu Nov 02 10:30:02 EDT 2023

FORMULA

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

STATUS

approved

editing

#8 by Alois P. Heinz at Mon Jul 17 09:46:35 EDT 2017

STATUS

editing

approved

#7 by Alois P. Heinz at Mon Jul 17 09:46:30 EDT 2017

LINKS

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

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

#6 by Alois P. Heinz at Mon Jul 17 09:43:33 EDT 2017

DATA

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

STATUS

proposed

editing

#5 by Jean-François Alcover at Mon Jul 17 09:28:54 EDT 2017

STATUS

editing

proposed

#4 by Jean-François Alcover at Mon Jul 17 09:28:42 EDT 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 *)

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 16:48:46 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com), _, Apr 29 2000

Discussion

Fri Mar 30

16:48

OEIS Server: https://oeis.org/edit/global/110

#2 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

N. J. A. Sloane (njas, (AT)research.att.com), Apr 29 2000

#1 by N. J. A. Sloane at Mon May 08 03:00:00 EDT 2000

NAME

Binomial transform of A000029.

DATA

OFFSET

0,2

KEYWORD

nonn

AUTHOR

njas, Apr 29 2000

STATUS

approved