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 A123900 #12 Jun 04 2019 09:32:00
%S A123900 6,12,60,180,2520,1008,18144,18144,3991680,5987520,155675520,
%T A123900 1089728640,26153487360,523069747200,17784371404800,12312257126400,
%U A123900 935731541606400,4678657708032,12772735542927360,140500090972200960
%N A123900 a(n) = (n+3)!/(d(n)*d(n+1)*d(n+2)) where d(n) = cancellation factor in reducing Sum_{k=0...n} 1/k! to lowest terms.
%H A123900 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 A123900 J. Sondow, <a href="https://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 A123900 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.
%F A123900 a(n) = (n+3)!/(A093101(n)*A093101(n+1)*A093101(n+2)) where A093101(n) = gcd(n!,1+n+n(n-1)+...+n!).
%e A123900 a(2) = 60 because (2+3)!/(d(2)*d(3)*d(4)) = 5!/(GCD(2,5)*GCD(6,16)*GCD(24,65)) = 120/2 = 60.
%t A123900 (A[n_] := If[n==0,1,n*A[n-1]+1]; d[n_] := GCD[A[n],n! ]; Table[(n+3)!/(d[n]*d[n+1]*d[n+2]), {n,0,21}])
%Y A123900 Cf. A000522, A061354, A093101, A123899, A123901.
%K A123900 easy,nonn
%O A123900 0,1
%A A123900 _Jonathan Sondow_, Oct 18 2006