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%I #18 Sep 08 2022 08:46:11
%S 70,126,294,846,2814,10326,40614,168126,723534,3208806,14570934,
%T 67417806,316645854,1505245686,7225414854,34956689886,170199537774,
%U 832952952966,4093454620374,20184631056366,99800366967294,494533989722646,2454868429675494
%N a(n) = 5*2^(n+2) + 2^(2n+2) + 10*3^n + 5^n + 35.
%C This is the sequence of fifth terms of "fourth partial sums of m-th powers".
%H Colin Barker, <a href="/A254367/b254367.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="/A254367/a254367_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 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
%F G.f.: -2*(2972*x^4-4302*x^3+2177*x^2-462*x+35) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - _Colin Barker_, Jan 30 2015
%t Table[5 2^(n + 2) + 2^(2 n + 2) + 10 3^n + 5^n + 35, {n, 0, 30}] (* _Vincenzo Librandi_, Feb 02 2015 *)
%o (PARI) vector(30, n, n--; 5*2^(n+2) + 2^(2*n+2) + 10*3^n + 5^n + 35) \\ _Colin Barker_, Jan 30 2015
%o (Magma) [5*2^(n+2)+2^(2*n+2)+10*3^n+5^n+35: n in [0..30]]; // _Vincenzo Librandi_, Feb 02 2015
%Y Cf. A140504, A254365, A254366.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 30 2015
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