%I #30 Apr 13 2018 11:20:22
%S 1,2,4,7,9,22,35,79,2992,3597,17523,28632,41470,53093,57406,14504930,
%T 42622213,188335162,322429556,1023003875,1328535963,3138645732,
%U 11618168524,137721814936,156929353744,166732460513,813398686532
%N Engel expansion of Pi^2/6, or zeta(2) = 1.64493.
%C Cf. A006784 for definition of Engel expansion.
%D F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
%H G. C. Greubel and T. D. Noe, <a href="/A059186/b059186.txt">Table of n, a(n) for n = 1..1000</a>[Terms 1 to 300 computed by T. D. Noe; Terms 301 to 1000 computed by G. C. Greubel, Dec 27 2016]
%H F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbruechen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
%H P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
%t NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
%t EngelExp[N[Pi^2/6, 7!], 100] (* Modified by _G. C. Greubel_, Dec 27 2016 *)
%Y Cf. A013661, A053980, A067912.
%K nonn,easy,nice
%O 1,2
%A _Mitch Harris_