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%I #30 Sep 08 2022 08:44:49
%S 1,2,5,13,34,89,232,596,1490,3588,8273,18228,38403,77533,150438,
%T 281403,509015,892926,1523117,2532359,4112704,6536993,10186540,
%U 15586342,23449376,34731776,50700937,73018870,103843433,145950389,202879594,279108997,380260541
%N a(n) = T(n, 2*n-10), T given by A027926.
%H Colin Barker, <a href="/A027933/b027933.txt">Table of n, a(n) for n = 5..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F a(n) = Sum_{k=0..5} binomial(n-k, 10-2*k). - _Len Smiley_, Oct 20 2001
%F a(n) = 34 -9161*n/280 -101897*n^3/20160 +794293*n^2/50400 -287*n^5/1280 +438209*n^4/362880 +5593*n^6/172800 -47*n^7/13440 -n^9/80640 +n^8/3780 +n^10/3628800. - _R. J. Mathar_, Oct 05 2009
%F G.f.: x^5*(1-x+x^2)*(1-5*x+9*x^2-5*x^3+x^4)*(1-3*x+5*x^2-3*x^3+x^4) / (1-x)^11. - _Colin Barker_, Feb 17 2016
%p seq(add(binomial(n-k, 10-2*k), k=0..5), n=5..40); # _G. C. Greubel_, Sep 27 2019
%t Table[Sum[Binomial[n-k, 10-2k], {k,0,5}], {n,5,40}] (* or *)
%t Drop[#, 5] &@ CoefficientList[Series[x^5(1-x+x^2)(1-5x+9x^2-5x^3+x^4)(1- 3x+5x^2-3x^3+x^4)/(1-x)^11, {x, 0, 37}], x] (* _Michael De Vlieger_, Feb 17 2016 *)
%o (PARI) Vec(x^5*(1-x+x^2)*(1-5*x+9*x^2-5*x^3+x^4)*(1-3*x+5*x^2-3*x^3+x^4) / (1-x)^11 + O(x^40)) \\ _Colin Barker_, Feb 17 2016
%o (PARI) vector(40, n, sum(k=0,5, binomial(n+4-k, 10-2*k)) ) \\ _G. C. Greubel_, Sep 27 2019
%o (Magma) [&+[Binomial(n-k, 10-2*k): k in [0..5]] : n in [5..40]]; // _G. C. Greubel_, Sep 27 2019
%o (Sage) [sum(binomial(n-k, 10-2*k) for k in (0..5)) for n in (5..40)] # _G. C. Greubel_, Sep 27 2019
%o (GAP) List([5..40], n-> Sum([0..5], k-> Binomial(n-k, 10-2*k)) ); # _G. C. Greubel_, Sep 27 2019
%Y Cf. A027926, A228074.
%K nonn,easy
%O 5,2
%A _Clark Kimberling_
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