This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A254684 #23 Oct 07 2015 15:52:04
%S A254684 1,133,2842,29274,197400,1001952,4137966,14597934,45454773,127861825,
%T A254684 330540028,795609724,1801339176,3867558072,7926516900,15591322404,
%U A254684 29566276257,54259095093,96674782246,167695627750,283882296880
%N A254684 Fifth partial sums of seventh powers (A001015).
%H A254684 Luciano Ancora, <a href="/A254684/b254684.txt">Table of n, a(n) for n = 1..1000</a>
%H A254684 Luciano Ancora, <a href="/A254640/a254640_1.pdf">Partial sums of m-th powers with Faulhaber polynomials</a>
%H A254684 Luciano Ancora, <a href="/A254647/a254647_2.pdf"> Pascal’s triangle and recurrence relations for partial sums of m-th powers </a>
%H A254684 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A254684 G.f.: (- x - 120*x^2 - 1191*x^3 - 2416*x^4 - 1191*x^5 - 120*x^6 - x^7)/(- 1 + x)^13.
%F A254684 a(n) = n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(-3 + 5*n + n^2)*(-2 + 5*n + n^2)*(5 + 5*n + n^2)/95040.
%F A254684 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + n^7.
%e A254684 First differences: 1, 127, 2060, 14324, 63801, ... (A152726)
%e A254684 ----------------------------------------------------------------------
%e A254684 The seventh powers: 1, 128, 2187, 16384, 78125, ... (A001015)
%e A254684 ----------------------------------------------------------------------
%e A254684 First partial sums: 1, 129, 2316, 18700, 96825, ... (A000541)
%e A254684 Second partial sums: 1, 130, 2446, 21146, 117971, ... (A250212)
%e A254684 Third partial sums: 1, 131, 2577, 23723, 141694, ... (A254641)
%e A254684 Fourth partial sums: 1, 132, 2709, 26432, 168126, ... (A254646)
%e A254684 Fifth partial sums: 1, 133, 2842, 29274, 197400, ... (this sequence)
%t A254684 Table[n (1 + n) (2 + n) (3 + n) (4 + n) (5 + n) (- 3 + 5 n + n^2) (- 2 + 5 n + n^2) (5 + 5 n + n^2)/95040, {n,21}] (* or *)
%t A254684 CoefficientList[Series[(- 1 - 120 x - 1191 x^2 - 2416 x^3 - 1191 x^4 - 120 x^5 - x^6)/(-1 + x)^13, {x,0,20}], x]
%o A254684 (PARI) a(n)=n*(1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(-3+5*n+n^2)*(-2+5*n+n^2)*(5+5*n+n^2)/95040 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A254684 Cf. A000541, A001015, A152726, A250212, A254641, A254646, A254681, A254682, A254683.
%K A254684 nonn,easy
%O A254684 1,2
%A A254684 _Luciano Ancora_, Feb 12 2015