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%I #8 Jul 30 2017 11:42:32
%S 0,1,97,962,4578,14979,38995,86996,173636,318597,547333,891814,
%T 1391270,2092935,3052791,4336312,6019208,8188169,10941609,14390410,
%U 18658666,23884427,30220443,37834908,46912204,57653645,70278221,85023342,102145582,121921423
%N Sum of n consecutive fourth powers starting with n^4.
%H Colin Barker, <a href="/A262925/b262925.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = n*(-1+70*n^2-225*n^3+186*n^4)/30.
%F G.f.: x*(16*x^4+241*x^3+395*x^2+91*x+1) / (x-1)^6.
%e a(3) = 3^4 + 4^4 + 5^4 = 962.
%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,97,962,4578,14979},30] (* _Harvey P. Dale_, Jul 30 2017 *)
%o (PARI) vector(40, n, n--; sum(k=n, 2*n-1, k^4))
%o (PARI) concat(0, Vec(x*(16*x^4+241*x^3+395*x^2+91*x+1)/(x-1)^6 + O(x^40)))
%Y Cf. A050410, A240137, A262926.
%K nonn,easy
%O 0,3
%A _Colin Barker_, Oct 04 2015
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