coincidence A064984 and series for Tan[x], almost

[Meeussen Wouter (bkarnd)]

found it:

A036279 as Denominator of the series coefficients of Tan[x] 'happens' to be
almost equal to the odd-indexed terms of sequence  A049606 = Denominator of
2^n/n!

exceptions occur at

Select[Range[100],GCD[2(-1+4^#)BernoulliB[2#],2 Denominator[4^#/ (2#)!]] >
#&]

{12, 20, 25, 28, 30, 34, 35, 36, 40, 44, 45, 49, 50, 51, 52, 54, 55, 56, 60,

62, 63, 65, 66, 68, 70, 72, 76, 77, 80, 81, 84, 85, 88, 90, 91, 92, 95, 98,
99, 100}

and that's why they differ. 
Almost, Pffft!



-----Original Message-----
From: Meeussen Wouter (bkarnd) 
Sent: woensdag 21 november 2001 19:44
To: Seqfan (E-mail)
Subject: coincidence A064984 and series for Tan[x], almost


as we are all aware (2^2^2^2 times now)
a coincidence between two seemingly unrelated formulas generating the same
sequence, is rare and (sometimes) interesting, but all to often just lack of
competence.

So, I was (incompetently) surprised to find the rowsums for the even rows in
A064984 to be:
1, 3, 15, 315, 2835, 155925, 6081075, 638512875, 10854718875, 1856156927625,

194896477400625, 49308808782358125, 3698160658676859375

and for the odd seriescoefficients for Tan[x]
1, 3, 15, 315, 2835, 155925, 6081075, 638512875, 10854718875, 1856156927625,

194896477400625, 2900518163668125, 3698160658676859375

their ratio (first 33 terms) being
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 527, 1, 1, 1, 1,
31, 1, 1, 731, 1, 41, 1, 1, 1  

anomalies at position 12, 20, 25, 28, 30,..


Wouter Meeussen
tel  +32 (0)51 332 124
fax +32 (0)51 332 175
mail: wouter.meeussen at vandemoortele.com




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