Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Sep 13 2024 17:02:37
%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 *)
%t LinearRecurrence[{16,-94,240,-225},{0,1,8,51},40] (* _Harvey P. Dale_, Sep 13 2024 *)
%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