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A082135
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Expansion of e.g.f. x*exp(4*x)*cosh(x).
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5
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0, 1, 8, 51, 304, 1765, 10104, 57239, 321248, 1787337, 9864040, 54035707, 294031632, 1590368429, 8556082136, 45812239455, 244255416256, 1297362967441, 6867617339592, 36243304518083, 190746485895920, 1001394643462773
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A082134. 4th binomial transform of (0,1,0,3,0,5,0,7,...).
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LINKS
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FORMULA
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a(n) = n*(3^(n-1) + 5^(n-1))/2.
E.g.f.: x*exp(4x)*cosh(x).
G.f.: x*(17*x^2-8*x+1) / ((3*x-1)^2*(5*x-1)^2). [Colin Barker, Dec 10 2012]
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MATHEMATICA
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With[{nn = 20}, CoefficientList[Series[x Exp[4*x] Cosh[x], {x, 0, nn}], x] Range[0, nn]!] (* T. D. Noe, Dec 10 2012 *)
Table[n*(3^(n-1)+5^(n-1))/2, {n, 0, 30}] (* G. C. Greubel, Feb 05 2018 *)
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PROG
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(PARI) for(n=0, 30, print1(n*(3^(n-1)+5^(n-1))/2, ", ")) \\ G. C. Greubel, Feb 05 2018
(Magma) [n*(3^(n-1)+5^(n-1))/2: n in [0..30]]; // G. C. Greubel, Feb 05 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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