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%I #11 Jun 13 2015 00:55:23
%S 126,210,450,1200,3750,13080,49350,197400,825750,3577080,15930150,
%T 72528600,336141750,1580449080,7518010950,36102667800,174710721750,
%U 850780489080,4164115131750,20465328135000,100917328245750,498984369457080,2472617583932550
%N a(n) = 35*2^n + 5*4^n + 15*3^n + 5^n + 70.
%C This is the sequence of fifth terms of "fifth partial sums of m-th powers".
%H Colin Barker, <a href="/A254370/b254370.txt">Table of n, a(n) for n = 0..1000</a>
%H Luciano Ancora, <a href="https://oeis.org/A254370/a254370.pdf">Demonstration of formulas</a>, page 2.
%H Luciano Ancora, <a href="/A254370/a254370_1.pdf">Recurrence relations for partial sums of m-th powers</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F G.f.: -6*(1879*x^4-2675*x^3+1335*x^2-280*x+21) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - _Colin Barker_, Jan 30 2015
%F a(n) = 15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5). - _Colin Barker_, Jan 30 2015
%t Table[35 2^n + 5 4^n + 15 3^n + 5^n + 70, {n, 0, 30}] (* _Bruno Berselli_, Jan 30 2015 *)
%o (PARI) vector(30, n, n--; 35*2^n + 5*4^n + 15*3^n + 5^n + 70) \\ _Colin Barker_, Jan 30 2015
%Y Cf. A168614, A254368, A254369.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 30 2015
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