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 A331612 #8 Aug 08 2023 14:52:16
%S A331612 1,1,14,481,30449,3064306,448104029,89621046061,23468873468054,
%T A331612 7786478152466221,3190021872763911149,1580829351026679822586,
%U A331612 931656913226081002622489,643808850722810399312420281,515431991397502094847830786174,473171296200788822261644150349881
%N A331612 E.g.f.: exp(1 / (2 - sec(x)) - 1) (even powers only).
%F A331612 a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n-1,2*k-1) * A002114(k) * a(n-k).
%F A331612 a(n) ~ 2^(2*n) * 3^(2*n + 1/8) * exp(-5/12 + sqrt(3)/(4*Pi) + 2*3^(1/4)*sqrt(n/Pi) - 2*n) * n^(2*n - 1/4) / Pi^(2*n + 1/4). - _Vaclav Kotesovec_, Jan 26 2020
%t A331612 nmax = 15; Table[(CoefficientList[Series[Exp[1/(2 - Sec[x]) - 1], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%t A331612 e[0] = 1; e[n_] := e[n] = (-1)^n (1 - Sum[(-1)^j Binomial[2 n, 2 j] 3^(2 (n - j)) e[j], {j, 0, n - 1}]); A002114[n_] := e[n]/2^(2 n + 1); a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n - 1, 2 k - 1] A002114[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]
%t A331612 With[{nn=40},Take[CoefficientList[Series[Exp[1/(2-Sec[x])-1],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Aug 08 2023 *)
%Y A331612 Cf. A000364, A002114, A217502, A331611.
%K A331612 nonn
%O A331612 0,3
%A A331612 _Ilya Gutkovskiy_, Jan 22 2020