OFFSET
0,2
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).
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).
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 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace((1+x)*exp(3*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018
(Magma) m:=30; R<x>:=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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 09 2003
STATUS
approved