Help needed
 

Please help in understanding the series 1, 2, 6, 8, 22, 32, 84, 128,... that is Sloane [URL="http://www.research.att.com/~njas/sequences/A081672"]A081672 [/URL]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

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.

[quote=AntonVrba;99792]Please help in understanding the series 1, 2, 6, 8, 22, 32, 84, 128,... that is Sloane [URL="http://www.research.att.com/~njas/sequences/A081672"]A081672 [/URL]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.
[/quote]
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)...

Friends, thanks the problem is solved

[URL="http://primepuzzles.redgolpe.com/topic.asp?TOPIC_ID=16"]see here[/URL]