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 A027950 #21 Sep 08 2022 08:44:49
%S A027950 1,6,63,344,1383,4685,14323,41119,113590,306605,816410,2157046,
%T A027950 5674578,14893364,39040633,102273950,267839033,701315739,1836198205,
%U A027950 4807389285,12586103720,32951083211,86267338468,225851160284,591286410708,1548008385490
%N A027950 a(n) = T(2n,n+2), T given by A027948.
%H A027950 Colin Barker, <a href="/A027950/b027950.txt">Table of n, a(n) for n = 2..1000</a>
%H A027950 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-26,45,-45,26,-8,1).
%F A027950 G.f.: x^2*(1-2*x+41*x^2-49*x^3+44*x^4-26*x^5+8*x^6-x^7)/((1-3*x+x^2)*(1-x)^5). - _Ralf Stephan_, Apr 24 2004
%F A027950 From _G. C. Greubel_, Sep 29 2019: (Start)
%F A027950 a(n) = Sum_{j=0..n-2} binomial(2*n-j, j+5), with a(2) = 1 for n >= 2.
%F A027950 a(n) = Fibonacci(2*n+6) - (48 + 47*n + 23*n^2 + 4*n^3 + 4*n^4)/6 for n >= 3. (End)
%p A027950 with(combinat); seq(`if`(n=2,1, fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6), n=2..40); # _G. C. Greubel_, Sep 29 2019
%t A027950 Table[If[n==2, 1, Fibonacci[2*n+6] -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6], {n,2,40}] (* _G. C. Greubel_, Sep 29 2019 *)
%t A027950 CoefficientList[Series[x^2(1-2x+41x^2-49x^3+44x^4-26x^5+8x^6-x^7)/ ((1-3x+x^2)(1-x)^5),{x,0,30}],x] (* or *) LinearRecurrence[{8,-26,45,-45,26,-8,1},{1,6,63,344,1383,4685,14323,41119},30] (* _Harvey P. Dale_, Aug 15 2021 *)
%o A027950 (PARI) Vec(x^2*(x^7-8*x^6+26*x^5-44*x^4+49*x^3-41*x^2+2*x-1)/((x-1)^5* (x^2-3*x+1)) + O(x^40)) \\ _Colin Barker_, Nov 19 2014
%o A027950 (PARI) vector(40, n, my(m=n+1); if(m==2, 1, fibonacci(2*m+6) -(48 +47*m +23*m^2 +4*m^3 +4*m^4)/6) ) \\ _G. C. Greubel_, Sep 29 2019
%o A027950 (Magma) [1] cat [Fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6: n in [3..40]]; // _G. C. Greubel_, Sep 29 2019
%o A027950 (Sage) [1]+[fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6 for n in (3..40)] # _G. C. Greubel_, Sep 29 2019
%o A027950 (GAP) Concatenation([1], List([3..40], n-> Fibonacci(2*n+6) -(48 +47*n +23*n^2 +4*n^3 +4*n^4)/6) ); # _G. C. Greubel_, Sep 29 2019
%Y A027950 Bisection of A053739.
%Y A027950 Cf. A000045, A027948.
%K A027950 nonn,easy
%O A027950 2,2
%A A027950 _Clark Kimberling_
%E A027950 More terms from _Colin Barker_, Nov 19 2014