This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113874 #24 Jun 04 2019 10:37:22
%S A113874 1,0,1,1,3,4,7,32,39,71,465,536,1001,8544,9545,18089,190435,208524,
%T A113874 398959,4996032,5394991,10391023,150869313,161260336,312129649,
%U A113874 5155334720,5467464369,10622799089,196677847971,207300647060
%N A113874 a(3n) = a(3n-1) + a(3n-2), a(3n+1) = 2n*a(3n) + a(3n-1), a(3n+2) = a(3n+1) + a(3n).
%C A113874 A113873(n)/a(n) -> e.
%C A113874 Without the first two terms, same as A007677 (denominators of convergents to e). - _Jonathan Sondow_, Aug 16 2006
%H A113874 T. D. Noe, <a href="/A113874/b113874.txt">Table of n, a(n) for n = 0..201</a>
%H A113874 H. Cohn, <a href="https://www.jstor.org/stable/27641837">A short proof of the simple continued fraction expansion of e</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 57-62.
%H A113874 J. Sondow, <a href="https://www.jstor.org/stable/27642006">A geometric proof that e is irrational and a new measure of its irrationality</a>, Amer. Math. Monthly 113 (2006) 637-641.
%H A113874 J. Sondow, <a href="http://arxiv.org/abs/0704.1282">A geometric proof that e is irrational and a new measure of its irrationality</a>, arXiv:0704.1282 [math.HO], 2007-2010.
%H A113874 J. Sondow and K. Schalm, <a href="http://arxiv.org/abs/0709.0671">Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II</a>, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.
%p A113874 a[0]:=1: a[1]:=0: a[2]:=1: for n from 3 to 34 do if n mod 3 = 0 then a[n]:=a[n-1]+a[n-2] elif n mod 3 = 1 then a[n]:=2*(n-1)*a[n-1]/3+a[n-2] else a[n]:=a[n-1]+a[n-2] fi: od: seq(a[n],n=0..34); # _Emeric Deutsch_, Jan 28 2006
%t A113874 a[0] = 1; a[1] = 0; a[n_] := a[n] = Switch[ Mod[n, 3], 0, a[n - 1] + a[n - 2], 1, 2(n - 1)/3*a[n - 1] + a[n - 2], 2, a[n - 1] + a[n - 2]]; a /@ Range[0, 30]
%t A113874 Join[{1,0},Denominator[Convergents[E,30]]] (* _Harvey P. Dale_, Aug 09 2014 *)
%Y A113874 Cf. A113873.
%K A113874 easy,nonn
%O A113874 0,5
%A A113874 _N. J. A. Sloane_, Jan 27 2006
%E A113874 More terms from _Robert G. Wilson v_ and _Emeric Deutsch_, Jan 28 2006