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Old 2007-03-03, 11:38   #1
AntonVrba
 
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Jun 2005

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Please help in understanding the series 1, 2, 6, 8, 22, 32, 84, 128,... that is Sloane A081672 and is titled "Expansion of exp(2x)-exp(0)+BesselI_0(2x)."

I do not understand the term "expansion" in above context.

Further do you recognize the following series in the same contents?
1,3,13, 27, 105, 243, 889, 3^7,....
1,4, 22, 64, 310, 1024, 4636, ...
1,5, 33, 125, 721, 3125, 16905, ...

These series I generate from any prime but in modula p.

best regards
Anton

Last fiddled with by AntonVrba on 2007-03-03 at 11:39
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Old 2007-03-05, 17:52   #2
ewmayer
2ω=0
 
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Glanced at the OEIS entry - it mentions an "Inverse binomial transform", so my guess is that that leads to an oo series, and these are the coefficients.

But don't take my (speculative) word for it - suggest you e-mail the entry author, whose e-address is attached to the entry.
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Old 2007-03-05, 18:06   #3
m_f_h
 
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Feb 2007

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Quote:
Originally Posted by AntonVrba View Post
Please help in understanding the series 1, 2, 6, 8, 22, 32, 84, 128,... that is Sloane A081672 and is titled "Expansion of exp(2x)-exp(0)+BesselI_0(2x)."

I do not understand the term "expansion" in above context.

Further do you recognize the following series in the same contents?
1,3,13, 27, 105, 243, 889, 3^7,....
1,4, 22, 64, 310, 1024, 4636, ...
1,5, 33, 125, 721, 3125, 16905, ...
These series I generate from any prime but in modula p.
I don't understand it, either; I suspect there might be error since why write exp(0) instead of 1 ?
I don't recognize your sequences either - modula p means "mod p" ?
then for primes smaller than 100 I dont understand how to get values > 100, and 'mod p' should give different things once you have a number larger than p (and before there's no use in saying mod p)...
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Old 2007-03-06, 10:55   #4
AntonVrba
 
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Jun 2005

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Friends, thanks the problem is solved

see here
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