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 A027981 #24 Jun 08 2025 17:32:50
%S A027981 1,10,40,124,340,868,2116,4996,11524,26116,58372,129028,282628,614404,
%T A027981 1327108,2850820,6094852,12976132,27525124,58195972,122683396,
%U A027981 257949700,541065220,1132462084,2365587460,4932501508,10267656196,21340618756,44291850244,91804925956,190052302852,392989507588,811748818948,1675037245444,3453153705988
%N A027981 a(n) = Sum_{k=0..2*n} (k+1)*T(n,k), T given by A027960.
%H A027981 G. C. Greubel, <a href="/A027981/b027981.txt">Table of n, a(n) for n = 0..1000</a>
%H A027981 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F A027981 a(2*n+1) = 6*(4*n+1) * 4^n + 4. - _Ralf Stephan_, Mar 22 2004
%F A027981 From _R. J. Mathar_, May 22 2013: (Start)
%F A027981 a(n) = 3*2^n*(2*n-1) + 4.
%F A027981 G.f.: (1 + 5*x - 2*x^2)/( (1-x)*(1-2*x)^2 ). (End)
%F A027981 a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3), with a(0)=1, a(1)=10, a(2)=40. - _Harvey P. Dale_, Apr 17 2015
%F A027981 E.g.f.: 3*(4*x - 1)*exp(2*x) + 4*exp(x). - _Ilya Gutkovskiy_, Apr 17 2016
%t A027981 LinearRecurrence[{5,-8,4},{1,10,40},30] (* _Harvey P. Dale_, Apr 17 2015 *)
%o A027981 (Magma)
%o A027981 A027981:= func< n | 3*2^n*(2*n-1) + 4 >; // _G. C. Greubel_, Jun 07 2025
%o A027981 (Python)
%o A027981 def A027981(n): return 3*2**n*(2*n-1) + 4 # _G. C. Greubel_, Jun 07 2025
%Y A027981 Cf. A027960.
%K A027981 nonn
%O A027981 0,2
%A A027981 _Clark Kimberling_
%E A027981 More terms added by _G. C. Greubel_, Jun 07 2025