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 A027982 #16 Jun 07 2025 18:35:26
%S A027982 1,10,38,108,270,632,1426,3148,6854,14784,31674,67508,143278,303016,
%T A027982 638882,1343388,2817942,5898128,12320650,25689988,53477246,111148920,
%U A027982 230686578,478150508,989855590,2046820192,4227858266,8724152148,17985175374,37044092744
%N A027982 a(n) = Sum_{k=0..2*n} (k+1)*T(n, 2*n-k), T given by A027960.
%H A027982 Colin Barker, <a href="/A027982/b027982.txt">Table of n, a(n) for n = 0..1000</a>
%H A027982 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A027982 From _Colin Barker_, Nov 25 2014: (Start)
%F A027982 a(n) = (-10 + 11*2^n + 2*(-3 + 2^n)*n).
%F A027982 a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).
%F A027982 G.f.: (1 + 4*x - 9*x^2 - 2*x^3) / ((1-x)^2*(1-2*x)^2). (End)
%F A027982 E.g.f.: (11 + 4*x)*exp(2*x) - 2*(5 + 3*x)*exp(x). - _G. C. Greubel_, Jun 07 2025
%t A027982 LinearRecurrence[{6,-13,12,-4},{1,10,38,108},40] (* _Harvey P. Dale_, Oct 28 2020 *)
%o A027982 (PARI) Vec((1+4*x-9*x^2-2*x^3)/((1-x)^2*(1-2*x)^2) + O(x^100)) \\ _Colin Barker_, Nov 25 2014
%o A027982 (Magma)
%o A027982 A027982:= func< n | (2*n+11)*2^n -2*(3*n+5) >; // _G. C. Greubel_, Jun 07 2025
%o A027982 (Python)
%o A027982 def A027982(n): return (2*n+11)*2**n -2*(3*n+5) # _G. C. Greubel_, Jun 07 2025
%Y A027982 Cf. A027960.
%K A027982 nonn,easy
%O A027982 0,2
%A A027982 _Clark Kimberling_
%E A027982 More terms from _Colin Barker_, Nov 25 2014