A364112 Expansion of e.g.f. 3*x/(exp(-3*x)+exp(-x)+exp(x))

0, 1, 2, -5, -28, 85, 806, -3185, -41656, 207913, 3428810, -20824925, -413027284, 2961364861, 68560259054, -567040692425, -15005357203312, 140642298254929, 4187120881320338, -43861384856264885, -1450918780756640140, 16798626454194814117, 611263061851828001462, -7751163512199032905505

Offset

0,3

Comments

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.

The terms of odd indices are related to the generalized Bernoulli numbers attached to the primitive Dirichlet character of period 3 (see A002111).

Links

Table of n, a(n) for n=0..23.

Formula

E.g.f.: 3*x/(exp(-3*x)+exp(-x)+exp(x)).

Prog

(Sage)
x = PowerSeriesRing(QQ, 'x').gen()
N = 20
f = (3*x/((-3*x).exp(N)+(-x).exp(N)+(x).exp(N))).egf_to_ogf()
print(list(f))
(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

Crossrefs

Very similar to A083007.

Related to A158073 and A002111.

Sequence in context: A326230 A095159 A047132 * A264699 A318590 A072371

Adjacent sequences: A364109 A364110 A364111 * A364113 A364114 A364115

Keyword

sign

Author

F. Chapoton, Jul 13 2023

Status

approved