[seqfan] e^(pi rt 163) series suggested by Bill Gosper (OEIS A178449)

Robert Munafo mrob27 at gmail.com
Thu Dec 23 23:54:06 CET 2010

(Moving discussion over to seqfan)

A178449 are coefficients for a series sum to "Ramanujan's constant" e^(pi *
sqrt(163)), suggested over in math-fun by Bill Gosper:

 Subject: e^(pi rt 163) =

s^3 + 744 - 196884/s^3 + 167975456/s^6 - 180592706130/s^9 +
> 217940004309743/s^12 - 19517553165954887/s^15 + 74085136650518742/s^18 - ...

where s = 640320.  Only the 1st three terms are in EIS.  Are the rest well
> defined?


I looked around the web for the numbers (167975456 etc.); NJAS created the

I added one link that I found, some code (using bc) that computes those
coefficients in a well-defined way, and the next term following the same

It seems I found a definition that produces those numbers, though maybe not
the intended definition?

Feel free to suggest something better (like more concise code perhaps :-) or
edit/comment on A178449.


- Robert

  Robert Munafo  --  mrob.com
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