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%I #10 Dec 26 2016 13:31:17
%S 1,4,21,38,117,7135,7809,1614095,3624914,8425892,16789093,18206374,
%T 20026429,106066483,297533015,329807820,393798971,762907505,
%U 98220075842,124475838767,132042717951,252079930415,308550332741,1938650338119,10430003444835,12126839108751
%N Pierce Expansion of tanh(1).
%H G. C. Greubel, <a href="/A280091/b280091.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>
%t PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[Tanh[1] , 7!], 50]
%Y Cf. A073744 (tanh(1)).
%K nonn
%O 1,2
%A _G. C. Greubel_, Dec 25 2016