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%I #18 Oct 21 2022 21:35:46
%S 1,47,144,328,640,1131,1863,2910,4359,6311,8882,12204,16426,21715,
%T 28257,36258,45945,57567,71396,87728,106884,129211,155083,184902,
%U 219099,258135,302502,352724,409358,472995,544261,623818,712365,810639,919416,1039512,1171784
%N a(n) = T(n, n-5), array T as in A055818.
%H Vincenzo Librandi, <a href="/A055822/b055822.txt">Table of n, a(n) for n = 5..5000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F From _Chai Wah Wu_, Dec 29 2016: (Start)
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 11.
%F G.f.: x^5*(1 + 41*x -123*x^2 + 149*x^3 - 93*x^4 + 30*x^5 - 4*x^6)/(1-x)^6. (End)
%F From _G. C. Greubel_, Jan 22 2020: (Start)
%F a(n) = (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120, for n>5, with a(5) = 1.
%F E.g.f.: (-480 -720*x -180*x^2 +60*x^3 +30*x^4 -4*x^5 + (480 +240*x -300*x^2 + 40*x^3 +20*x^4 +x^5)*exp(x))/120. (End)
%p seq( `if`(n=5, 1, (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120), n=5..50); # _G. C. Greubel_, Jan 22 2020
%t Join[{1,47,144,328,640}, LinearRecurrence[{6,-15,20,-15,6,-1}, {1131,1863,2910, 4359,6311,8882}, 5004]] (* _Vincenzo Librandi_, Dec 30 2016 *)
%t Table[If[n==5, 1, (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120], {n,5,50}] (* _G. C. Greubel_, Jan 22 2020 *)
%o (Magma) I:=[1,47,144,328,640,1131,1863,2910,4359,6311, 8882]; [n le 11 select I[n] else 6*Self(n-1)-15*Self(n-2) +20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2016
%o (PARI) vector(45, n, my(m=n+4); if(m==5, 1, (480 +524*m -250*m^2 -45*m^3 +10*m^4 +m^5)/120)) \\ _G. C. Greubel_, Jan 22 2020
%o (Sage) [1]+[(480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120 for n in (6..50)] # _G. C. Greubel_, Jan 22 2020
%o (GAP) Concatenation([1], List([6..50], n-> (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120 )); # _G. C. Greubel_, Jan 22 2020
%Y Cf. A055818.
%K nonn,easy
%O 5,2
%A _Clark Kimberling_, May 28 2000
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