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 A349265 #16 Oct 30 2024 01:55:26
%S A349265 2,4,30,272,3522,55744,1066590,23750912,604935042,17328937984,
%T A349265 551609685150,19313964388352,737740947722562,30527905292468224,
%U A349265 1360427147514751710,64955605537174126592,3308161927353377294082,179013508069217017790464,10256718523496425979562270
%N A349265 Generalized Euler numbers, a(n) = n!*[x^n](sec(5*x)*(sin(x) + sin(3*x) + cos(2*x) + cos(4*x))).
%C A349265 For references and examples see A349264.
%H A349265 Matthew House, <a href="/A349265/b349265.txt">Table of n, a(n) for n = 0..377</a>
%t A349265 m = 18; CoefficientList[Series[Sec[5*x] * (Sin[x] + Sin[3*x] + Cos[2*x] + Cos[4*x]), {x, 0, m}], x] * Range[0, m]! (* _Amiram Eldar_, Nov 20 2021 *)
%o A349265 (Sage)
%o A349265 t = PowerSeriesRing(QQ, 't', default_prec=19).gen()
%o A349265 f = (sin(t) + sin(3*t) + cos(2*t) + cos(4*t)) / cos(5*t)
%o A349265 f.egf_to_ogf().list()
%o A349265 (PARI) seq(n)={my(x='x + O('x^(n+1))); Vec(serlaplace((sin(x) + sin(3*x) + cos(2*x) + cos(4*x))/cos(5*x)))} \\ _Andrew Howroyd_, Nov 20 2021
%Y A349265 Row 5 of A349271.
%Y A349265 Cf. A000111, A001589, A007289, A349264, A001587.
%K A349265 nonn
%O A349265 0,1
%A A349265 _Peter Luschny_, Nov 20 2021