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%I #17 Sep 08 2022 08:45:09
%S 0,1,8,51,304,1765,10104,57239,321248,1787337,9864040,54035707,
%T 294031632,1590368429,8556082136,45812239455,244255416256,
%U 1297362967441,6867617339592,36243304518083,190746485895920,1001394643462773
%N Expansion of e.g.f. x*exp(4*x)*cosh(x).
%C Binomial transform of A082134. 4th binomial transform of (0,1,0,3,0,5,0,7,...).
%H G. C. Greubel, <a href="/A082135/b082135.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-94,240,-225).
%F a(n) = n*(3^(n-1) + 5^(n-1))/2.
%F E.g.f.: x*exp(4x)*cosh(x).
%F G.f.: x*(17*x^2-8*x+1) / ((3*x-1)^2*(5*x-1)^2). [_Colin Barker_, Dec 10 2012]
%t With[{nn = 20}, CoefficientList[Series[x Exp[4*x] Cosh[x], {x, 0, nn}], x] Range[0, nn]!] (* _T. D. Noe_, Dec 10 2012 *)
%t Table[n*(3^(n-1)+5^(n-1))/2, {n,0,30}] (* _G. C. Greubel_, Feb 05 2018 *)
%o (PARI) for(n=0,30, print1(n*(3^(n-1)+5^(n-1))/2, ", ")) \\ _G. C. Greubel_, Feb 05 2018
%o (Magma) [n*(3^(n-1)+5^(n-1))/2: n in [0..30]]; // _G. C. Greubel_, Feb 05 2018
%Y Cf. A082133, A082136.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Apr 06 2003
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