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 A322604 #12 Feb 16 2025 08:33:57
%S A322604 1,1,1,2,3,4,2,4,7,5,6,5,12,1,12,9,0,7,4,14,10,17,2,14,23,4,2,2,16,2,
%T A322604 10,18,23,26,26,26,24,1,17,26,18,12,0,15,42,34,39,33,20,18,40,43,12,
%U A322604 47,51,10,50,35,14,23,16,1,55,41,34,29,14,41,35,60,53,45,61,35,49,73,13,13,57,59
%N A322604 Factorial expansion of exp(gamma) = Sum_{n>=1} a(n)/n! with a(n) as large as possible.
%C A322604 Gamma is the Euler-Mascheroni constant (A001620).
%H A322604 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicExpansion.html">Harmonic Expansion</a>
%H A322604 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Fa#facbase">Index entries for factorial base representation</a>
%F A322604 Sum_{n>=1} a(n)/n! = exp(gamma) = A073004.
%e A322604 exp(gamma) = 1 + 1/2! + 1/3! + 2/4! + 3/5! + 4/6! + 2/7! + 4/8! + ...
%p A322604 Digits:=200: a:=n->`if`(n=1,floor(exp(gamma)),floor(factorial(n)*exp(gamma))-n*floor(factorial(n-1)*exp(gamma))): seq(a(n),n=1..100); # _Muniru A Asiru_, Dec 20 2018
%t A322604 With[{b = Exp[EulerGamma]}, Table[If[n==1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]
%o A322604 (PARI) default(realprecision, 250); b = exp(Euler); for(n=1, 80, print1( if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
%Y A322604 Cf. A073004 (decimal expansion), A094644 (continued fraction), A001620 (Euler-Mascheroni constant).
%K A322604 nonn
%O A322604 1,4
%A A322604 _Tristan Cam_, Dec 20 2018