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%I #46 Nov 24 2019 16:13:53
%S 2,5,5,1,3,25,1,1,17,1,3,3,1,12,1,8,5,3,1,46,3,4,12,1,5,22,3,2,1,7,4,
%T 2,1,13,13,8,1,1,3,1,1,1,2,1,11,1,5,2,1,4,7,1,71,1,1,1,6,1,1,1,1,1,1,
%U 1,4,6,1,9,1,1,1,6,1,1,1,5,1,1,1,5,1,1,1,1,1,2,2,1,1,5,2,1,2,10,1,19,2,2,4,1
%N Continued fraction expansion of exp(Pi/4).
%C This value arises naturally by taking the ratio of the volume of a unit 2n-dimensional ball to the volume of the 2n-dimensional cube containing it (with side length 2) and summing over all n.
%H Greg Egan, <a href="https://twitter.com/gregeganSF/status/1160461092973211648">Puzzle in which this value arises naturally</a>
%H Grant Sanderson and Brady Haran, <a href="https://www.youtube.com/watch?v=6_yU9eJ0NxA">Darts in Higher Dimensions</a>, Numberphile video (2019)
%t ContinuedFraction[Exp[Pi/4], 100]
%o (PARI) contfrac(exp(Pi/4)) \\ _Felix Fröhlich_, Aug 28 2019
%Y Cf. A160510 (decimal expansion), A058287, A087299, A329912 (Engel expansion).
%K nonn,cofr,easy
%O 0,1
%A _Grant T Sanderson_, Aug 28 2019