A082307 Expansion of e.g.f. (1+x)*exp(3*x)*cosh(x).

1, 4, 16, 66, 280, 1208, 5248, 22816, 98944, 427392, 1838080, 7870976, 33568768, 142637056, 604045312, 2550276096, 10737713152, 45097779200, 188979871744, 790276734976, 3298540650496, 13743907405824, 57174629810176

Offset: 0

Author

Paul Barry, Apr 09 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A002306; a(n)=(A082308(n)+A079028(n))/2

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-52,96,-64).

Crossrefs

Cf. A082308.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(3*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[3*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(3*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018

Formula

a(n) = ((n+2)*2^(n-1) + (n+4)*4^(n-1))/2.

G.f.: ((1-3x)/(1-4x)^2 + (1-x)/(1-2x)^2)/2.

E.g.f. (1+x)*exp(3*x)*cosh(x).