A082306 Expansion of e.g.f. (1+x)*exp(2*x)*cosh(x).

1, 3, 9, 29, 97, 327, 1097, 3649, 12033, 39371, 127945, 413349, 1328609, 4251535, 13551753, 43046729, 136314625, 430467219, 1355971721, 4261625389, 13366006881, 41841412823, 130754415049, 407953774929, 1270932914177

Offset: 0

Author

Paul Barry, Apr 09 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A082305 a(n)=(A006234(n)+A000027(n))/2

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-22,24,-9).

Crossrefs

Cf. A082307.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(2*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[2*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(2*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018

Formula

a(n) = (n + 1 + 3^(n-1)*(n + 3))/2.

G.f.: (1/(1-x)^2 + (1-2*x)/(1-3*x)^2)/2.

E.g.f.: (1+x)*exp(2*x)*cosh(x).