cp's OEIS Frontend

A206810 Sum_{0

%I A206810 #19 Jun 17 2017 03:53:56
%S A206810 15,145,670,2146,5501,12131,23996,43716,74667,121077,188122,282022,
%T A206810 410137,581063,804728,1092488,1457223,1913433,2477334,3166954,4002229,
%U A206810 5005099,6199604,7611980,9270755,11206845,13453650,16047150
%N A206810 Sum_{0<j<n} (n^4-j^4).
%C A206810 For a guide to related sequences, see A206817.
%H A206810 Danny Rorabaugh, <a href="/A206810/b206810.txt">Table of n, a(n) for n = 2..10000</a>
%H A206810 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A206810 a(n) = n^5-p(n), where p(n) is the n-th partial sum of (j^4).
%F A206810 a(n) = t(n)-t(n-1), where t = A206811.
%F A206810 a(n) = (n-10*n^3-15*n^4+24*n^5)/30. G.f.: x^2*(x^3+25*x^2+55*x+15) / (x-1)^6. - _Colin Barker_, Jul 11 2014
%e A206810 a(2) = 2^4-1^4 = 15.
%e A206810 a(3) = (3^4-1^4) + (3^4-2^4) = 145.
%t A206810 s[k_] := k^4; t[1] = 0;
%t A206810 p[n_] := Sum[s[k], {k, 1, n}];
%t A206810 c[n_] := n*s[n] - p[n];
%t A206810 t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
%t A206810 Table[c[n], {n, 2, 50}]  (* A206810  *)
%t A206810 Flatten[Table[t[n], {n, 2, 35}]] (* A206811 *)
%o A206810 (PARI) Vec(x^2*(x^3+25*x^2+55*x+15)/(x-1)^6 + O(x^100)) \\ _Colin Barker_, Jul 11 2014
%o A206810 (Sage) [sum([n^4-j^4 for j in range(1,n)]) for n in range(2,30)] # _Danny Rorabaugh_, Apr 18 2015
%Y A206810 Cf. A206817, A206811.
%K A206810 nonn,easy
%O A206810 2,1
%A A206810 _Clark Kimberling_, Feb 15 2012