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%I #17 Sep 08 2022 08:44:49
%S 3,7,18,47,123,319,806,1954,4506,9859,20495,40615,77040,140455,247085,
%T 420906,696509,1122751,1767344,2722551,4112177,6100063,8900312,
%U 12789498,18121132,25342683,35015477,47837823,64671742
%N T(n, 2n-9), T given by A027960.
%H Colin Barker, <a href="/A027971/b027971.txt">Table of n, a(n) for n = 5..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = (17055360 -16329024*n +7697736*n^2 -2299060*n^3 +462798*n^4 -60207*n^5 +4284*n^6 -30*n^7 -18*n^8 +n^9)/362880. - _Colin Barker_, Nov 25 2014
%F G.f.: x^5*(3-2*x)*(1 -7*x +23*x^2 -44*x^3 +55*x^4 -44*x^5 +23*x^6 -7*x^7 +x^8)/(1-x)^10. - _Colin Barker_, Nov 25 2014
%p seq(coeff(series(x^5*(3-2*x)*(1 -7*x +23*x^2 -44*x^3 +55*x^4 -44*x^5 +23*x^6 -7*x^7 +x^8)/(1-x)^10, x, n+1), x, n), n = 5..40); # _G. C. Greubel_, Sep 26 2019
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1}, {3,7,18,47, 123,319,806,1954,4506,9859},40] (* _Harvey P. Dale_, Aug 04 2017 *)
%o (PARI) Vec(-x^5*(2*x-3)*(x^8-7*x^7+23*x^6-44*x^5+55*x^4-44*x^3+23*x^2 -7*x+1)/(x-1)^10 + O(x^40)) \\ _Colin Barker_, Nov 25 2014
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^5*(3 -2*x)*(1-7*x+23*x^2-44*x^3+55*x^4-44*x^5+23*x^6-7*x^7+x^8)/(1-x)^10 )); // _G. C. Greubel_, Sep 26 2019
%o (Sage)
%o def A027971_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x^5*(3-2*x)*(1-7*x+23*x^2-44*x^3+55*x^4-44*x^5+23*x^6-7*x^7 +x^8)/(1-x)^10 ).list()
%o a=A027971_list(40); a[5:] # _G. C. Greubel_, Sep 26 2019
%o (GAP) a:=[3,7,18,47, 123,319,806,1954,4506,9859];; for n in [11..40] do a[n]:=10*a[n-1]-45*a[n-2]+120*a[n-3]-210*a[n-4]+252*a[n-5]-210*a[n-6] +120*a[n-7] -45*a[n-8]+10*a[n-9]-a[n-10]; od; a; # _G. C. Greubel_, Sep 26 2019
%Y A column of triangle A027011.
%K nonn,easy
%O 5,1
%A _Clark Kimberling_
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