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%I #20 Jun 13 2015 00:55:23
%S 126,252,672,2232,8592,36552,166992,804552,4037712,20923272,111231312,
%T 603667272,3331889232,18646768392,105558814032,603280840392,
%U 3475274371152,20152803339912,117513698083152,688425727971912,4048693055291472,23888489018765832,141334996634766672,838119509472869832
%N a(n) = 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56.
%C This is the sequence of sixth terms of "fourth partial sums of m-th powers".
%H Colin Barker, <a href="/A254465/b254465.txt">Table of n, a(n) for n = 0..1000</a>
%H Luciano Ancora, <a href="/A254367/a254367.pdf">Demonstration of formulas</a>, page 2.
%H Luciano Ancora, <a href="/A254364/a254364_1.pdf">Recurrence relations for partial sums of m-th powers</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).
%F G.f.: -6*(10036*x^5 -16454*x^4 +10065*x^3 -2905*x^2 +399*x -21) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - _Colin Barker_, Jan 31 2015
%F a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - _Colin Barker_, Jan 31 2015
%t Table[35 2^n + 10 4^n + 20 3^n + 4 5^n + 6^n + 56, {n, 0, 24}] (* _Michael De Vlieger_, Jan 31 2015 *)
%o (PARI) vector(30, n, n--; 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56) \\ _Colin Barker_, Jan 31 2015
%Y Cf. A140504, A254365, A254366, A254367, A254466.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 31 2015
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