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%I #16 Sep 08 2022 08:44:49
%S 1,4,11,29,76,196,487,1148,2552,5353,10636,20120,36425,63415,106630,
%T 173821,275603,426242,644593,955207,1389626,1987886,2800249,3889186,
%U 5331634,7221551,9672794,12822346,16833919,21901961,28256096
%N a(n) = T(n, 2*n-8), T given by A027960.
%H Colin Barker, <a href="/A027970/b027970.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F Sequence satisfies an 8-degree polynomial approximating A002878.
%F a(n) = (-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320. - _Colin Barker_, Nov 25 2014
%F G.f.: x^4*(x^8-5*x^7+11*x^6-10*x^5-x^4+10*x^3-11*x^2+5*x-1) / (x-1)^9. - _Colin Barker_, Nov 25 2014
%F From _G. C. Greubel_, Jul 01 2019: (Start)
%F a(n) = A027971(n+1) - A027971(n).
%F E.g.f.: (1169280 + 443520*x + 80640*x^2 + 6720*x^3 +(-1169280 +725760*x -221760*x^2 +47040*x^3 -6720*x^4 +1008*x^5 -56*x^6 +16*x^7 +x^8)*exp(x) )/8!. (End)
%t Table[(-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320, {n, 4, 40}] (* _G. C. Greubel_, Jul 01 2019 *)
%o (PARI) Vec(x^4*(x^8-5*x^7+11*x^6-10*x^5-x^4+10*x^3-11*x^2+5*x-1)/(x-1)^9 + O(x^40)) \\ _Colin Barker_, Nov 25 2014
%o (PARI) for(n=4,40, print1((-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320, ", ")) \\ _G. C. Greubel_, Jul 01 2019
%o (Magma) [(-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320: n in [4..40]]; // _G. C. Greubel_, Jul 01 2019
%o (Sage) [(-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320 for n in (4..40)] # _G. C. Greubel_, Jul 01 2019
%o (GAP) List([4..40], n-> (-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320) # _G. C. Greubel_, Jul 01 2019
%Y A column of triangle A026998.
%K nonn,easy
%O 4,2
%A _Clark Kimberling_
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