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A027954 a(n) = T(2n+1, n+2), T given by A027948.

%I A027954 #13 Sep 08 2022 08:44:49
%S A027954 1,5,41,189,674,2098,6050,16703,44995,119575,315460,829060,2174596,
%T A027954 5698329,14924829,39081553,102326310,267905078,701397990,1836299475,
%U A027954 4807512695,12586252715,32951261576,86267550344,225851410184,591286703533,1548008726545,4052739505253,10610209821610
%N A027954 a(n) = T(2n+1, n+2), T given by A027948.
%H A027954 G. C. Greubel, <a href="/A027954/b027954.txt">Table of n, a(n) for n = 1..1000</a>
%H A027954 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,26,-19,7,-1).
%F A027954 G.f.: x*(1 -2*x +25*x^2 -29*x^3 +19*x^4 -7*x^5 +x^6)/((1-x)^4*(1 -3*x +x^2)). - _Colin Barker_, Nov 25 2014
%F A027954 From _G. C. Greubel_, Sep 30 2019: (Start)
%F A027954 a(n) = Sum_{j=0..n-1} binomial(2*n-j+1, j+4) for n >= 2.
%F A027954 a(n) = Fibonacci(2*n+6) - (24 + 23*n + 12*n^2 + 4*n^3)/3 for n >= 2. (End)
%p A027954 with(combinat); seq(`if`(n=1,1, fibonacci(2*n+6) -(24 +23*n +12*n^2 +4*n^3)/3), n=1..40); # _G. C. Greubel_, Sep 30 2019
%t A027954 Table[If[n==1, 1, Fibonacci[2*n+6] - (24 +23*n +12*n^2 +4*n^3)/3], {n, 1, 40}] (* _G. C. Greubel_, Sep 30 2019 *)
%o A027954 (PARI) vector(40, n, if(n==1, 1, fibonacci(2*n+6) -(24 +23*n +12*n^2 + 4*n^3)/3 )) \\ _G. C. Greubel_, Sep 30 2019
%o A027954 (Magma) [1] cat [Fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3: n in [2..40]]; // _G. C. Greubel_, Sep 30 2019
%o A027954 (Sage) [1]+[fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3 for n in (2..40)] # _G. C. Greubel_, Sep 30 2019
%o A027954 (GAP) Concatenation([1], List([2..40], n-> Fibonacci(2*n+6) -(24 + 23*n + 12*n^2 + 4*n^3)/3 )); # _G. C. Greubel_, Sep 30 2019
%Y A027954 Cf. A000045, A027948.
%K A027954 nonn
%O A027954 1,2
%A A027954 _Clark Kimberling_
%E A027954 Name corrected and terms a(22) onward by _G. C. Greubel_, Sep 30 2019