A082309 Expansion of e.g.f.: (1+x)*exp(5*x)*cosh(x).
1, 6, 36, 218, 1336, 8280, 51776, 325792, 2057856, 13023104, 82456576, 521826816, 3298727936, 20822038528, 131210919936, 825373859840, 5182772248576, 32487861092352, 203308891897856, 1270289732337664, 7924975155019776
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (20,-148,480,-576).
Programs
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Magma
m:=30; R
:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(5*x)*Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Sep 16 2018 -
Mathematica
With[{nn=30},CoefficientList[Series[(1+x)Exp[5x]Cosh[x],{x,0,nn}],x]Range[0,nn]!] (* or *) LinearRecurrence[{20,-148,480,-576},{1,6,36,218},30] (* Harvey P. Dale, Aug 27 2012 *) -
PARI
x='x+O('x^30); Vec(serlaplace((1+x)*exp(5*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018
Formula
a(n) = ((n+4)*4^(n-1) + (n+6)*6^(n-1))/2.
G.f.: ((1-5*x)/(1-6*x)^2 + (1-3*x)/(1-4*x)^2)/2.
From Harvey P. Dale, Aug 27 2012: (Start)
E.g.f.: (1+x)*exp(5*x)*cosh(x).
a(n) = 20*a(n-1) - 148*a(n-2) + 480*a(n-3) - 576*a(n-4), n>3. (End)
Extensions
Definition clarified by Harvey P. Dale, Aug 27 2012
Comments