cp's OEIS Frontend

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.

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

Original entry on oeis.org

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

Views

Author

F. Chapoton, Jul 13 2023

Keywords

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).

Crossrefs

Very similar to A083007.
Related to A158073 and A002111.

Programs

  • 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
  • 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))

Formula

E.g.f.: 3*x/(exp(-3*x)+exp(-x)+exp(x)).
Previous Showing 11-11 of 11 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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