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A082309
Expansion of e.g.f.: (1+x)*exp(5*x)*cosh(x).
2
1, 6, 36, 218, 1336, 8280, 51776, 325792, 2057856, 13023104, 82456576, 521826816, 3298727936, 20822038528, 131210919936, 825373859840, 5182772248576, 32487861092352, 203308891897856, 1270289732337664, 7924975155019776
OFFSET
0,2
COMMENTS
Binomial transform of A082307.
FORMULA
a(n) = (A081106(n) + A079028(n))/2.
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)
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 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace((1+x)*exp(5*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018
(Magma) m:=30; R<x>:=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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 09 2003
EXTENSIONS
Definition clarified by Harvey P. Dale, Aug 27 2012
STATUS
approved