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 A101684 #17 Nov 30 2023 02:55:35
%S A101684 0,1,0,3,4,3,6,7,6,9,10,8,12,13,11,15,16,15,18,19,18,21,22,19,24,25,
%T A101684 22,27,28,27,30,31,30,33,34,32,36,37,35,39,40,39,42,43,42,45,46,42,48,
%U A101684 49,45,51,52,51,54,55,54,57,58,56,60,61,59,63,64,63,66,67,66,69,70,67
%N A101684 Exponent of 2 in denominators of expansion of e.g.f.: exp(-1 + sqrt(1+x)).
%H A101684 Robert Israel, <a href="/A101684/b101684.txt">Table of n, a(n) for n = 0..10000</a>
%F A101684 2^a(n) is denominator of c(n) where c(n) = (c(n-2) - (4*n-6)*c(n-1))/4, c(0) = 1, c(1) = 1/2. - _Robert Israel_, Nov 30 2023
%p A101684 S:= series(exp(-1+sqrt(1+x)), x, 201):
%p A101684 seq(padic:-ordp(denom(n!*coeff(S,x,n)),2), n=0..200); # _Robert Israel_, Nov 30 2023
%t A101684 IntegerExponent[Denominator[With[{nn=80},CoefficientList[ Series[ Exp[ -1+Sqrt[1+x]],{x,0,nn}],x] Range[0,nn]!]],2] (* _Harvey P. Dale_, Aug 04 2021 *)
%o A101684 (PARI) my(x='x+O('x^30)); apply(x->(valuation(denominator(x), 2)), Vec(serlaplace(exp(sqrt(1+x)-1)))) \\ _Michel Marcus_, Nov 30 2023
%Y A101684 First differences are in A101685. Cf. A101683.
%K A101684 nonn
%O A101684 0,4
%A A101684 _Ralf Stephan_, Dec 13 2004
%E A101684 Definition clarified by _Harvey P. Dale_, Aug 04 2021