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A082308
Expansion of e.g.f. (1+x)*exp(4*x)*cosh(x).
3
1, 5, 25, 127, 657, 3449, 18281, 97395, 519841, 2773741, 14776377, 78538343, 416367665, 2201517153, 11610231433, 61078202971, 320570884929, 1678897264085, 8775159682649, 45780628812879, 238431945108433
OFFSET
0,2
COMMENTS
Binomial transform of A082307.
FORMULA
a(n) = (A081105(n) + A006234(n))/2.
a(n) = ((n+3)*3^(n-1) + (n+5)*5^(n-1))/2.
G.f.: ((1-4*x)/(1-5*x)^2 + (1-2*x)/(1-3*x)^2)/2.
E.g.f.: (1+x)*exp(4*x)*cosh(x) = (1+x)*(exp(5*x) + exp(3*x))/2.
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[(1 + x)*Exp[4*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(4*x)*cosh(x))) \\ G. C. Greubel, Sep 16 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(4*x)*Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Sep 16 2018
CROSSREFS
Cf. A082309.
Sequence in context: A099524 A081916 A307879 * A270767 A026718 A060928
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 09 2003
STATUS
approved