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%I #21 Jun 13 2015 00:55:23
%S 56,126,378,1386,5778,26226,126378,636426,3314178,17714466,96660378,
%T 536249466,3015243378,17141522706,98333399178,568324150506,
%U 3305074833378,19319850386946,113420243462778,668241096915546,3948892688324178,23393955029043186
%N a(n) = 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21.
%C This is the sequence of sixth terms of "third partial sums of m-th powers".
%H Colin Barker, <a href="/A254463/b254463.txt">Table of n, a(n) for n = 0..1000</a>
%H Luciano Ancora, <a href="https://oeis.org/A254364/a254364.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.: -2*(12276*x^5 -20578*x^4 +12831*x^3 -3766*x^2 +525*x -28) / ((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[15 2^n + 6 4^n + 10 3^n + 3 5^n + 6^n + 21, {n, 0, 25}] (* _Michael De Vlieger_, Jan 31 2015 *)
%o (PARI) vector(30, n, n--; 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21) \\ _Colin Barker_, Jan 31 2015
%Y Cf. A062709, A254362, A254363, A254364, A254464.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 31 2015
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