Constant C=0.1688... for A081881 seems to be wrong

[Rainer Rosenthal]

Thanks to Neil's latest update I am proud to
announce A136616 and A136617, dealing with
harmonic numbers.

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# 1. Extending A081881
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A related sequence is Wouter Meeussen's A081881.
Using the relation with A136617 and the nice
formula from David Cantrell there, it is easy to
extend this sequence from 12 elements now to many
more. The first 40 elements are:

1, 2, 4, 10, 26, 69, 186, 504, 1369, 3720, 10111,
27483, 74705, 203068, 551995, 1500477, 4078718,
11087104, 30137872, 81923228, 222690421, 605335323,
1645472007, 4472856655, 12158484965, 33050188741,
89839727480, 244209698681, 663830786257, 1804479163453,
4905082919846, 13333397768101, 36243932864644,
98521224097850, 267808453182726, 727978851794328,
1978851684335001, 5379076574743407, 14621846107014725,
39746298571222758, 108041641154662534

The Maple code is:
restart:Digits:=50:e:=exp(1);A136617 := n -> 
floor( (e - 1)*(n - 1/2) + (e - 1/e)/(24*(n - 1/2)) );
apq := n -> n + A136617(n);A081881 := n -> (apq@@n)(1);
seq(A081881(n),n=0..40);

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# 2. Checking Benoit Cloitre's formula
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The FORMULA section in A081881 says:
a(n) is asymptotic to C*exp(n) where C=0.1688...
- Benoit Cloitre (abmt(AT)wanadoo.fr), Apr 14 2003

Numerical evidence suggests that this limit exists:

                        a(n)
         C  =   lim   -------
               n->oo      n
                         e

but the value is  C = 0.4589991659480974... as it seems
and not 0.1688...

I would like to add my Maple code to A081881 and give a
cross reference to A136617 and David Cantrell's formula.
At the same time I would like to correct the formula of
Benoit Cloitre. But I may be wrong and so I ask you as
SeqFan.

Best regards,
Rainer Rosenthal
r.rosenthal at web.de