This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082135 #19 Sep 13 2024 17:02:37
%S A082135 0,1,8,51,304,1765,10104,57239,321248,1787337,9864040,54035707,
%T A082135 294031632,1590368429,8556082136,45812239455,244255416256,
%U A082135 1297362967441,6867617339592,36243304518083,190746485895920,1001394643462773
%N A082135 Expansion of e.g.f. x*exp(4*x)*cosh(x).
%C A082135 Binomial transform of A082134. 4th binomial transform of (0,1,0,3,0,5,0,7,...).
%H A082135 G. C. Greubel, <a href="/A082135/b082135.txt">Table of n, a(n) for n = 0..1000</a>
%H A082135 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-94,240,-225).
%F A082135 a(n) = n*(3^(n-1) + 5^(n-1))/2.
%F A082135 E.g.f.: x*exp(4x)*cosh(x).
%F A082135 G.f.: x*(17*x^2-8*x+1) / ((3*x-1)^2*(5*x-1)^2). [_Colin Barker_, Dec 10 2012]
%t A082135 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 A082135 Table[n*(3^(n-1)+5^(n-1))/2, {n,0,30}] (* _G. C. Greubel_, Feb 05 2018 *)
%t A082135 LinearRecurrence[{16,-94,240,-225},{0,1,8,51},40] (* _Harvey P. Dale_, Sep 13 2024 *)
%o A082135 (PARI) for(n=0,30, print1(n*(3^(n-1)+5^(n-1))/2, ", ")) \\ _G. C. Greubel_, Feb 05 2018
%o A082135 (Magma) [n*(3^(n-1)+5^(n-1))/2: n in [0..30]]; // _G. C. Greubel_, Feb 05 2018
%Y A082135 Cf. A082133, A082136.
%K A082135 easy,nonn
%O A082135 0,3
%A A082135 _Paul Barry_, Apr 06 2003