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 A101683 #24 Nov 30 2023 02:55:19
%S A101683 1,1,0,1,-5,9,-329,3655,-11961,721315,-12310199,29326887,-4939227215,
%T A101683 113836841041,-356357531655,77087063678521,-2238375706930349,
%U A101683 17366683494629835,-2294640596998068569,80381887628910919255
%N A101683 Write exp(sqrt(1+x)-1) = Sum c(n) x^n/n!; then a(n) = numerator of c(n).
%C A101683 Odd part of A000806.
%H A101683 Robert Israel, <a href="/A101683/b101683.txt">Table of n, a(n) for n = 0..404</a>
%F A101683 Numerator of c(n) satisfying c(n) = (c(n-2) - (4*n-6)*c(n-1))/4, c(0) = 1, c(1) = 1/2. - _Robert Israel_, Nov 30 2023
%e A101683 exp(sqrt(1+x)-1) = 1+(1/2)*x+(1/48)*x^3-(5/384)*x^4+(3/320)*x^5-(329/46080)*x^6+(731/129024)*x^7-(1329/286720)*x^8+... - From _N. J. A. Sloane_, Aug 29 2012
%p A101683 c[0]:= 1: c[1]:= 1/2:
%p A101683 for n from 2 to 100 do c[n]:= (c[n-2]-(4*n-6)*c[n-1])/4 od:
%p A101683 seq(numer(c[n]),n=0..100); # _Robert Israel_, Nov 30 2023
%t A101683 With[{nn=20},Numerator[CoefficientList[Series[Exp[Sqrt[1+x]-1],{x,0,nn}],x]Range[0,nn]!]] (* _Harvey P. Dale_, Aug 29 2012 *)
%o A101683 (PARI) my(x='x+O('x^30)); apply(numerator, Vec(serlaplace(exp(sqrt(1+x)-1)))) \\ _Michel Marcus_, Nov 30 2023
%Y A101683 Denominators are 2^A101684(n).
%K A101683 sign,frac
%O A101683 0,5
%A A101683 _Ralf Stephan_, Dec 13 2004
%E A101683 Definition clarified by _N. J. A. Sloane_, Aug 29 2012