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

0,2

Comments

Binomial transform of A082307.

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).

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

Cf. A082308, A082307, A082306, A082305.

Sequence in context: A196869 A172489 A033142 * A004319 A129324 A180218

Adjacent sequences: A082306 A082307 A082308 * A082310 A082311 A082312

Keyword

easy,nonn

Author

Paul Barry, Apr 09 2003

Extensions

Definition clarified by Harvey P. Dale, Aug 27 2012

Status

approved