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%I #17 Jun 13 2015 00:55:23
%S 210,462,1386,5214,22770,110022,571626,3136014,17944290,106156182,
%T 645091866,4006997214,25344197010,162737255142,1058251916106,
%U 6955456112814,46130658756930,308314670926902,2074188361172346,14032607275346814,95392686703000050
%N a(n) = 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84.
%C This is the sequence of seventh terms of "fourth partial sums of m-th powers".
%H Colin Barker, <a href="/A254466/b254466.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_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).
%F G.f.: -6*(110440*x^6 -199272*x^5 +139840*x^4 -49405*x^3 +9345*x^2 -903*x +35) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - _Colin Barker_, Jan 31 2015
%F a(n) = 28*a(n-1) -322*a(n-2) +1960*a(n-3) -6769*a(n-4) +13132*a(n-5) -13068*a(n-6) +5040*a(n-7). - _Colin Barker_, Jan 31 2015
%t Table[56 2^n + 20 4^n + 35 3^n + 4 6^n + 10 5^n + 7^n + 84, {n, 0, 24}] (* _Michael De Vlieger_, Jan 31 2015 *)
%o (PARI) vector(30, n, n--; 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84) \\ _Colin Barker_, Jan 31 2015
%Y Cf. A140504, A254365, A254366, A254367, A254465.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 31 2015
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