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 A012458 #18 Aug 25 2025 10:23:45
%S A012458 2,-16,488,-30336,3303072,-556926720,135234491520,-44790227865600,
%T A012458 19434264780034560,-10703464305128755200,7296385856008015226880,
%U A012458 -6031102564833737842851840,5942962739028147945628999680
%N A012458 Expansion of e.g.f. arcsin(arctan(x)^2), even powers only.
%H A012458 Vaclav Kotesovec, <a href="/A012458/b012458.txt">Table of n, a(n) for n = 0..210</a>
%F A012458 a(n) ~ (-1)^n * 2^(2*n + 3/2) * (exp(2) + 1)^(2*n + 5/2) * n^(2*n+1) / (exp(2*n+1) * (exp(2) - 1)^(2*n + 3/2)). - _Vaclav Kotesovec_, Aug 25 2025
%e A012458 2/2!*x^2 - 16/4!*x^4 + 488/6!*x^6 - 30336/8!*x^8...
%t A012458 With[{nn=30}, Take[CoefficientList[Series[ArcSin[ArcTan[x]^2], {x,0,nn}], x] Range[0,nn]!, {3,-1,2}]] (* _Harvey P. Dale_, Dec 13 2011 *)
%K A012458 sign,changed
%O A012458 0,1
%A A012458 Patrick Demichel (patrick.demichel(AT)hp.com)
%E A012458 Definition corrected by _Harvey P. Dale_, Dec 13 2011
%E A012458 Name edited by _Jason Yuen_, Aug 25 2025