decode sequence
Gottfried Helms
Annette.Warlich at t-online.de
Mon Aug 20 19:53:01 CEST 2007
Dear seqfans -
I have a difficult sequence, not in OEIS:
let n begin at 1, then I have the sequence:
a(n)= 1/2 -1/12 1/48 -1/180 11/8640 -1/6720 -11/241920 29/1451520
493/43545600 -2711/239500800 -6203/3592512000 2636317/373621248000
-10597579/10461394944000 -439018457/78460462080000 ...
if I rescale
b(n) = a(n)*n*n! *(n+1)!
I seem to get integers:
b(n)= 1 -1 3 -16 110 -540 -9240 292320
14908320 -1639612800 -33013854720 21046667685120
-549927873855360 -637881314775344640
another rescaling, perhaps a bit more smooth, is
c(n) = a(n)*((n+1)!)^2
c(n)= 2 -3 12 -80 660 -3780 -73920 2630880
149083200 -18035740800 -396166256640 273606679906560
-7698990233975040 -9568219721630169600 ...
I can create this series by matrix-logarithm and exponentiation
to some finite extent, but to discuss things analytically it would
be good to have a more direct description.
Someone an idea?
Context:
It occurs in the core of a tetration-formula, where
f_s: x:= s^x - 1
and f_s is iterated. The special interest of these coefficients is,
that they allow to define a powerseries in y,x,log(s) for fractional
iterates of f_s, where y denotes the fractional value for the iteration.
Gottfried
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