|
|
A082306
|
|
Expansion of e.g.f. (1+x)*exp(2*x)*cosh(x).
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
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).
|
|
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 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace((1+x)*exp(2*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018
(Magma) m:=30; R<x>:=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
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|