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.

Showing 1-2 of 2 results.

A292757 Expansion of e.g.f. exp(x)*(1+tan(x))/((1-tan(x))*(tan(x)+sec(x))).

Original entry on oeis.org

1, 2, 4, 15, 72, 467, 3534, 31675, 321832, 3692927, 46988914, 658330035, 10056866292, 166476324887, 2967375285294, 56673879465595, 1154538708267952, 24990204586402847, 572731801523141674, 13855288923332516355, 352821804274904668812, 9433763230045116440807, 264251645557758720762054
Offset: 0

Views

Author

N. J. A. Sloane, Sep 26 2017

Keywords

Links

Crossrefs

Cf. A000834.

Programs

  • Mathematica
    nmax = 20; CoefficientList[Series[Exp[x]*(1+Tan[x])/((1-Tan[x])*(Tan[x]+Sec[x])), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 02 2019 *)

Formula

a(n) ~ 2^(2*n + 3) * n^(n + 1/2) / ((2 + sqrt(2)) * Pi^(n + 1/2) * exp(n - Pi/4)). - Vaclav Kotesovec, Jun 02 2019

A343843 a(n) = Sum_{k=0..n} (-1)^k*binomial(n, k)*A000831(k).

Original entry on oeis.org

1, -1, 1, -9, 33, -241, 1761, -15929, 161473, -1853281, 23584321, -330371049, 5047404513, -83546832721, 1489242229281, -28442492633369, 579425286625153, -12541705195066561, 287434687338368641, -6953491183101074889, 177069197398959999393, -4734481603905334522801
Offset: 0

Views

Author

Peter Luschny, May 06 2021

Keywords

Crossrefs

Cf. A000831, A000834, A109449.

Programs

  • Maple
    a := n -> add((-1)^k*binomial(n, k)*A000831(k), k=0..n):
seq(a(n), n = 0..21);
  • Mathematica
    Table[-1 + Sum[(-1)^k * Binomial[n, k] * 4^k * Abs[EulerE[k,1/2] + EulerE[k,1]], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, May 06 2021 *)

Formula

a(n) = (-2)^n*Sum_{k=0..n} A109449(n, k)*(-1/2)^k.
From Vaclav Kotesovec, May 06 2021: (Start)
a(n) ~ (-1)^n * exp(-Pi/4) * 4^(n+1) * n! / Pi^(n+1).
E.g.f.: exp(x)*(1 - tan(x))/(1 + tan(x)). (End)
Showing 1-2 of 2 results.

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

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