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 A364112 #23 Jun 02 2025 15:26:54
%S A364112 0,1,2,-5,-28,85,806,-3185,-41656,207913,3428810,-20824925,-413027284,
%T A364112 2961364861,68560259054,-567040692425,-15005357203312,140642298254929,
%U A364112 4187120881320338,-43861384856264885,-1450918780756640140,16798626454194814117,611263061851828001462,-7751163512199032905505
%N A364112 Expansion of e.g.f. 3*x/(exp(-3*x)+exp(-x)+exp(x)).
%C A364112 The terms of even indices are related to Bernoulli numbers. For example, 413027284 = 2^2 * 23 * 73 * 89 * 691 and 15005357203312 = 2^4 * 7 * 31 * 41 * 151 * 193 * 3617.
%C A364112 The terms of odd indices are related to the generalized Bernoulli numbers attached to the primitive Dirichlet character of period 3 (see A002111).
%F A364112 E.g.f.: 3*x/(exp(-3*x)+exp(-x)+exp(x)).
%o A364112 (Sage)
%o A364112 x = PowerSeriesRing(QQ, 'x').gen()
%o A364112 N = 20
%o A364112 f = (3*x/((-3*x).exp(N)+(-x).exp(N)+(x).exp(N))).egf_to_ogf()
%o A364112 print(list(f))
%o A364112 (PARI) my(N=25, x='x+O('x^N)); Vec(serlaplace(3*x/(exp(-3*x)+exp(-x)+exp(x))), -N) \\ _Michel Marcus_, Jul 13 2023
%Y A364112 Very similar to A083007.
%Y A364112 Related to A158073 and A002111.
%K A364112 sign
%O A364112 0,3
%A A364112 _F. Chapoton_, Jul 13 2023