cp's OEIS Frontend

A027969 a(n) = T(n, 2*n-7), T given by A027960.

%I A027969 #13 Sep 08 2022 08:44:49
%S A027969 3,7,18,47,120,291,661,1404,2801,5283,9484,16305,26990,43215,67191,
%T A027969 101782,150639,218351,310614,434419,598260,812363,1088937,1442448,
%U A027969 1889917,2451243,3149552,4011573,5068042,6354135,7909931,9780906,12018459,14680471,17831898,21545399,25902000,30991795
%N A027969 a(n) = T(n, 2*n-7), T given by A027960.
%H A027969 G. C. Greubel, <a href="/A027969/b027969.txt">Table of n, a(n) for n = 4..1000</a>
%H A027969 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A027969 From _Ralf Stephan_, Feb 07 2004: (Start)
%F A027969 G.f.: x^4*(3-2x)*(1-x+x^2)*(1-4x+7x^2-4x^3+x^4)/(1-x)^8.
%F A027969 First differences of A027970. (End)
%F A027969 From _G. C. Greubel_, Jul 01 2019: (Start)
%F A027969 a(n) = (90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040.
%F A027969 E.g.f.: (-90720 - 35280*x - 7560*x^2 - 1680*x^3 + (90720 - 55440*x + 17640*x^2 - 3360*x^3 + 630*x^4 - 42*x^5 + 14*x^6 + x^7)*exp(x))/5040. (End)
%t A027969 Table[(90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040, {n,4,50}] (* _G. C. Greubel_, Jul 01 2019 *)
%o A027969 (PARI) for(n=4,50, print1((90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040, ", ")) \\ _G. C. Greubel_, Jul 01 2019
%o A027969 (Magma) [(90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040: n in [4..50]]; // _G. C. Greubel_, Jul 01 2019
%o A027969 (Sage) [(90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040 for n in (4..50)] # _G. C. Greubel_, Jul 01 2019
%o A027969 (GAP) List([4..50], n-> (90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040) # _G. C. Greubel_, Jul 01 2019
%Y A027969 A column of triangle A027011.
%K A027969 nonn
%O A027969 4,1
%A A027969 _Clark Kimberling_
%E A027969 Terms a(35) onward added by _G. C. Greubel_, Jul 01 2019