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 A000318 M3713 N1517 #46 Jun 22 2022 09:25:26
%S A000318 4,128,16384,4456448,2080374784,1483911200768,1501108249821184,
%T A000318 2044143848640217088,3605459138582973251584,7995891855149741436305408,
%U A000318 21776918737280678860353961984,71454103701490016776039304265728,278008871543597996197497752082448384
%N A000318 Generalized tangent numbers d(4,n).
%D A000318 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000318 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000318 T. D. Noe, <a href="/A000318/b000318.txt">Table of n, a(n) for n = 1..100</a>
%H A000318 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223295-5">Generalized Euler and class numbers</a>. Math. Comp. 21 (1967) 689-694.
%H A000318 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227093-9">Corrigenda to: "Generalized Euler and class numbers"</a>, Math. Comp. 22 (1968), 699
%H A000318 D. Shanks, <a href="/A000003/a000003.pdf">Generalized Euler and class numbers</a>, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]
%H A000318 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PadeApproximant.html">Padé approximants</a>.
%F A000318 a(n) = 2^(4n-2) * A000182(n).
%F A000318 The g.f. has the following continued fraction expansion: g.f. = [4, b(0), c(0), b(1), c(1), b(2), c(2), ...] where b(n) = (Sum_{k=0..n} 1/(2*k+1))^2 / (128*(n+1)*x), c(n) = -4/((2*n+3)*(Sum_{k=0..n} 1/(2*k+1))*(Sum_{k=0..n+1} 1/(2*k+1))) and each convergent of this continued fraction is a Padé approximant of the Maclaurin series Sum_{k>=1} a(n)*x^(n-1). - _Thomas Baruchel_, Oct 19 2005
%F A000318 a(n) = (2*n-1)!*[x^(2*n-1)](sec(4*x)*sin(4*x)). - _Peter Luschny_, Nov 21 2021
%p A000318 egf := sec(4*x)*sin(4*x): ser := series(egf, x, 26):
%p A000318 seq((2*n-1)!*coeff(ser, x, 2*n-1), n = 1..12); # _Peter Luschny_, Nov 21 2021
%t A000318 nn = 30; t = Rest@Union[Range[0, nn - 1]! CoefficientList[Series[Tan[x], {x, 0, nn}], x]]; t2 = t*2^Range[2, 2*nn, 4] (* _T. D. Noe_, Jun 19 2012 *)
%Y A000318 Cf. A000182, A000191, A000490, A349264.
%K A000318 nonn,easy
%O A000318 1,1
%A A000318 _N. J. A. Sloane_
%E A000318 More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000