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 2007-03-03, 11:38 #1 AntonVrba     Jun 2005 2·72 Posts Help needed 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
 2007-03-05, 17:52 #2 ewmayer ∂2ω=0     Sep 2002 República de California 5·2,351 Posts 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.
2007-03-05, 18:06   #3
m_f_h

Feb 2007

24×33 Posts

Quote:
 Originally Posted by AntonVrba 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)...

 2007-03-06, 10:55 #4 AntonVrba     Jun 2005 2×72 Posts Friends, thanks the problem is solved see here

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