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 A012780 #15 Sep 02 2022 09:46:02
%S A012780 1,3,45,1743,133305,17089083,3302755365,896199578823,324729845802225,
%T A012780 151401766241310963,88276508686397289885,62925559543228826845503,
%U A012780 53835082550295989275314345,54438337988081689498005862443,64228314189095958231926869651605
%N A012780 Expansion of e.g.f. arcsin(tan(x)) (odd powers only).
%C A012780 arcsin(sec(x)*sin(x)) = x + 3/3!*x^3 + 45/5!*x^5 + 1743/7!*x^7 + ...
%C A012780 arccos(tan(x)) = Pi/2 - x - 3*x^3/3! - 45*x^5/5! - 1743*x^7/7! - ...
%F A012780 (8 + z1)*z3 = - 96*z2 + 9*z2^2 - 256*z1 + 72*z2*z1 + 288*z1^2 + 6*z2*z1^2 + 48*z1^2 + z1^4 where z1 = f'(x)^2, z2 = f''(x)^2, z3 = f'''(x)^2, and f(x) = arcsin(tan(x)). - _Michael Somos_, Sep 01 2022
%F A012780 a(n) = (2n+1)! * [x^(2n+1)] arcsin(tan(x)). - _Alois P. Heinz_, Sep 02 2022
%t A012780 a[ n_] := If[ n<0, 0, (2*n+1)! * SeriesCoefficient[ ArcSin @ Tan @ x, {x, 0, 2*n+1}]]; (* _Michael Somos_, Sep 01 2022 *)
%o A012780 (PARI) {a(n) = if( n<0, 0, (2*n+1)! * polcoeff( asin( tan(x + O(x^(2*n+2)))), 2*n+1))}; /* _Michael Somos_, Sep 01 2022 */
%K A012780 nonn
%O A012780 0,2
%A A012780 Patrick Demichel (patrick.demichel(AT)hp.com)
%E A012780 Name clarified by _Joerg Arndt_, Sep 02 2022