%I #11 Sep 08 2022 08:44:49
%S 1,10,231,2300,14820,72905,298925,1077748,3540913,10871723,31775031,
%T 89633545,246575109,666605513,1781049298,4721874921,12456394685,
%U 32758238316,85985810716,225446971141,590714939822,1547211717890,4051642877482,10608719012366,27775885869046
%N a(n) = T(2n,n+4), T given by A027948.
%H G. C. Greubel, <a href="/A027952/b027952.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (12,-64,201,-414,588,-588,414,-201,64,-12,1).
%F From _G. C. Greubel_, Sep 29 2019: (Start)
%F a(n) = Sum_{j=0..n-3} binomial(2*n-j, j+9), with a(4) = 1.
%F a(n) = Fibonacci(2*n+10) - (138600 +133530*n +63999*n^2 + 20286*n^3 + 5929*n^4 + 616*n^6 - 96*n^7 + 16*n^8)/2520.
%F G.f.: x^4*(1 - 2*x + 175*x^2 - 33*x^3 + 408*x^4 - 614*x^5 + 587*x^6 - 414*x^7 + 201*x^8 - 64*x^9 + 12*x^10 - x^11)/((1-x)^9*(1-3*x+x^2)). (End)
%p with(combinat); seq(`if`(n=4,1, fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520), n=4..40); # _G. C. Greubel_, Sep 29 2019
%t Table[If[n==4, 1, Fibonacci[2*n+10] - (138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520], {n, 4, 40}] (* _G. C. Greubel_, Sep 29 2019 *)
%o (PARI) vector(40, n, my(m=n+3); if(m==4, 1, fibonacci(2*m+10) -(138600 +133530*m +63999*m^2 + 20286*m^3 +5929*m^4 +616*m^6 -96*m^7 +16*m^8)/2520) ) \\ _G. C. Greubel_, Sep 29 2019
%o (Magma) [1] cat [Fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520: n in [5..40]]; // _G. C. Greubel_, Sep 29 2019
%o (Sage) [1]+[fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520 for n in (5..40)] # _G. C. Greubel_, Sep 29 2019
%o (GAP) Concatenation([1], List([5..40], n-> Fibonacci(2*n+10) -(138600 +133530*n +63999*n^2 + 20286*n^3 +5929*n^4 +616*n^6 -96*n^7 +16*n^8)/2520) ); # _G. C. Greubel_, Sep 29 2019
%Y Cf. A000045, A027948.
%K nonn
%O 4,2
%A _Clark Kimberling_
%E Terms a(23) onward added by _G. C. Greubel_, Sep 29 2019