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A082307
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Expansion of e.g.f. (1+x)*exp(3*x)*cosh(x).
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4
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1, 4, 16, 66, 280, 1208, 5248, 22816, 98944, 427392, 1838080, 7870976, 33568768, 142637056, 604045312, 2550276096, 10737713152, 45097779200, 188979871744, 790276734976, 3298540650496, 13743907405824, 57174629810176
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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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).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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