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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A082308 Expansion of e.g.f. (1+x)*exp(4*x)*cosh(x).

Original entry on oeis.org

1, 5, 25, 127, 657, 3449, 18281, 97395, 519841, 2773741, 14776377, 78538343, 416367665, 2201517153, 11610231433, 61078202971, 320570884929, 1678897264085, 8775159682649, 45780628812879, 238431945108433
Offset: 0

Views

Author

Paul Barry, Apr 09 2003

Keywords

Comments

Binomial transform of A082307.

Links

Crossrefs

Cf. A082309.

Programs

  • Magma
    m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(4*x)*Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Sep 16 2018
  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[(1 + x)*Exp[4*x]*Cosh[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Sep 16 2018 *)
  • PARI
    x='x+O('x^30); Vec(serlaplace((1+x)*exp(4*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018

Formula

a(n) = (A081105(n) + A006234(n))/2.
a(n) = ((n+3)*3^(n-1) + (n+5)*5^(n-1))/2.
G.f.: ((1-4*x)/(1-5*x)^2 + (1-2*x)/(1-3*x)^2)/2.
E.g.f.: (1+x)*exp(4*x)*cosh(x) = (1+x)*(exp(5*x) + exp(3*x))/2.
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