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 A068453 #16 Sep 08 2022 08:45:05 %S A068453 1,1,0,3,2,5,0,4,3,9,8,2,8,0,10,15,2,10,8,19,12,4,18,23,8,4,21,15,17, %T A068453 1,11,19,7,25,15,3,20,5,24,25,35,9,12,25,26,22,23,11,43,46,6,0,25,27, %U A068453 30,6,14,20,33,5,30,23,42,4,11,19,55,63,43,12,52,51,22,29,11,8,19,35,25 %N A068453 Factorial expansion of sqrt(e) = Sum_{n>=1} a(n)/n!. %H A068453 G. C. Greubel, <a href="/A068453/b068453.txt">Table of n, a(n) for n = 1..10000</a> %t A068453 With[{b = Sqrt[E]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *) %o A068453 (PARI) vector(30,n,if(n>1,t=t%1*n,t=exp(.5))\1) \\ _M. F. Hasler_, Nov 25 2018 %o A068453 (PARI) default(realprecision, 250); b = sqrt(exp(1)); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ _G. C. Greubel_, Nov 26 2018 %o A068453 (Magma) SetDefaultRealField(RealField(250)); [Floor(Sqrt(Exp(1)))] cat [Floor(Factorial(n)*Sqrt(Exp(1))) - n*Floor(Factorial((n-1))* Sqrt(Exp(1))) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018 %o A068453 (Sage) %o A068453 def A068453(n): %o A068453 if (n==1): return floor(sqrt(e)) %o A068453 else: return expand(floor(factorial(n)*sqrt(e)) - n*floor(factorial(n-1)*sqrt(e))) %o A068453 [A068453(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018 %Y A068453 Cf. A067840 (e^2), A075874 (Pi). %K A068453 easy,nonn %O A068453 1,4 %A A068453 _Benoit Cloitre_, Mar 10 2002 %E A068453 Name edited and keyword cons removed by _M. F. Hasler_, Nov 25 2018