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A254464 a(n) = 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28.

%I A254464 #26 Oct 18 2024 18:25:44
%S A254464 84,210,714,2982,14178,73470,404634,2331462,13906578,85232910,
%T A254464 533860554,3403329942,22012307778,144090486750,952693102074,
%U A254464 6352175272422,42655384385778,288161867586990,1956674663089194,13344181547374902,91343993647708578,627261876368085630
%N A254464 a(n) = 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28.
%C A254464 This is the sequence of seventh terms of "third partial sums of m-th powers".
%H A254464 Colin Barker, <a href="/A254464/b254464.txt">Table of n, a(n) for n = 0..1000</a>
%H A254464 Luciano Ancora, <a href="https://oeis.org/A254364/a254364.pdf">Demonstration of formulas</a>, page 2.
%H A254464 Luciano Ancora, <a href="/A254364/a254364_1.pdf">Recurrence relations for partial sums of m-th powers</a>.
%H A254464 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).
%F A254464 From _Colin Barker_, Jan 31 2015: (Start)
%F A254464 G.f.: -6*(40188*x^6 - 74058*x^5 + 52931*x^4 - 19005*x^3 + 3647*x^2 - 357*x + 14)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)).
%F A254464 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). (End)
%F A254464 E.g.f.: exp(x)*(exp(x)*(exp(5*x) + 3*exp(4*x) + 6*exp(3*x) + 10*exp(2*x) + 15*exp(x) + 21) + 28). - _Elmo R. Oliveira_, Sep 16 2024
%t A254464 Table[21 2^n + 10 4^n + 15 3^n + 3 6^n + 6 5^n + 7^n + 28, {n, 0, 24}] (* _Michael De Vlieger_, Jan 31 2015 *)
%t A254464 LinearRecurrence[{28,-322,1960,-6769,13132,-13068,5040},{84,210,714,2982,14178,73470,404634},30] (* _Harvey P. Dale_, May 17 2019 *)
%o A254464 (PARI) vector(30, n, n--; 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28) \\ _Colin Barker_, Jan 31 2015
%Y A254464 Cf. A062709, A254362, A254363, A254364, A254463.
%K A254464 nonn,easy
%O A254464 0,1
%A A254464 _Luciano Ancora_, Jan 31 2015