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 A217260 #26 Oct 14 2023 12:01:03
%S A217260 1,-1,1,0,-6,30,-90,0,2520,-22680,113400,0,-7484400,97297200,
%T A217260 -681080400,0,81729648000,-1389404016000,12504636144000,0,
%U A217260 -2375880867360000,49893498214560000,-548828480360160000
%N A217260 Expansion of e.g.f. 2*arctan(1+x) - Pi/2.
%H A217260 Robert Israel, <a href="/A217260/b217260.txt">Table of n, a(n) for n = 1..477</a>
%F A217260 E.g.f.: 2*arctan(1+x) - Pi/2.
%F A217260 a(n) = n!*(Sum_{i=1..floor(n+1)/2} ((-1)^(n+i)*binomial(n-1, 2*i-2))/(2*i-1))/2^(n-1).
%F A217260 E.g.f. is the series reversion of sec(x) + tan(x) - 1.
%F A217260 From _Robert Israel_, Jan 17 2017: (Start)
%F A217260 a(n) = (n-1)*a(n-1) - (n-1)*(n-2)*a(n-2)/2.
%F A217260 a(n) = 2^(1-n/2)*(n-1)!*sin(3*Pi*n/4). (End)
%p A217260 seq(2^(1-n/2)*sin(3/4*Pi*n)*(n-1)!, n=1..50); # _Robert Israel_, Jan 17 2017
%t A217260 Table[2^(1 - n/2)*(n - 1)!*Sin[3*Pi*n/4], {n, 30}] (* _Wesley Ivan Hurt_, Oct 14 2023 *)
%o A217260 (Maxima)
%o A217260 a(n):=n!*sum(((-1)^(n+i)*binomial(n-1,2*i-2))/(2*i-1),i,1,(n+1)/2)/2^(n-1);
%Y A217260 Cf. A000111 (e.g.f. sec(x)+tan(x)), A009775.
%K A217260 sign
%O A217260 1,5
%A A217260 _Vladimir Kruchinin_, Mar 17 2013