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 A131951 #23 Mar 03 2025 13:35:05
%S A131951 1,6,14,26,44,72,118,198,344,620,1154,2202,4276,8400,16622,33038,
%T A131951 65840,131412,262522,524706,1049036,2097656,4194854,8389206,16777864,
%U A131951 33555132,67109618,134218538,268436324,536871840,1073742814,2147484702,4294968416,8589935780
%N A131951 a(n) = 2^n + n*(n+3).
%C A131951 Row sums of triangle A131950.
%H A131951 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A131951 Binomial transform of (1, 5, 3, 1, 1, 1, ...).
%F A131951 G.f.: ( 1+x-7*x^2+3*x^3 ) / ( (2*x-1)*(x-1)^3 ). - _R. J. Mathar_, Apr 04 2012
%F A131951 E.g.f.: exp(x)*(exp(x) + x*(4 + x)). - _Stefano Spezia_, Mar 03 2025
%e A131951 a(3) = 26 = sum of row 3 terms, triangle A131950: (7 + 6 + 6 + 7).
%e A131951 a(3) = 26 = (1, 3, 3, 1) dot (1, 5, 3, 1) = (1 + 15 + 9 + 1).
%t A131951 LinearRecurrence[{5,-9,7,-2},{1, 6, 14, 26},34] (* _James C. McMahon_, Mar 02 2025 *)
%Y A131951 Cf. A131950.
%K A131951 nonn,easy
%O A131951 0,2
%A A131951 _Gary W. Adamson_, Jul 30 2007
%E A131951 New definition by _R. J. Mathar_, Apr 04 2012
%E A131951 a(28)-a(34) from _James C. McMahon_, Mar 02 2025