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%I #15 Dec 26 2016 05:31:14
%S 1,13,15,19,132,1474,1977,10392,12992,44777,59412,170685,217607,
%T 704791,818133,1387423,2208674,3206215,12732462,13962681,24593168,
%U 39744274,55804517,130269696,426536424,546807194,1030799587,1139987135
%N Engel expansion of zeta(4) = Pi^4/90 = Sum_{i>0} 1/i^4.
%H G. C. Greubel, <a href="/A067912/b067912.txt">Table of n, a(n) for n = 1..1000</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]]; EngelExp[N[Pi^4/90, 7!], 20] (* _G. C. Greubel_, Dec 26 2016 *)
%Y See A006784 for explanation of Engel expansions.
%Y Cf. A059186, A053980.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Mar 03 2002
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