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 A254683 #26 Jun 13 2015 00:55:24
%S A254683 1,69,1064,8736,49350,216342,787968,2489448,7024407,18074875,43072848,
%T A254683 96186272,203145852,408774588,788378400,1464523344,2631173181,
%U A254683 4587701601,7785938104,12894168000,20882898530,33138238770
%N A254683 Fifth partial sums of sixth powers (A001014).
%H A254683 Luciano Ancora, <a href="/A254683/b254683.txt">Table of n, a(n) for n = 1..1000</a>
%H A254683 Luciano Ancora, <a href="/A254640/a254640_1.pdf">Partial sums of m-th powers with Faulhaber polynomials</a>
%H A254683 Luciano Ancora, <a href="/A254647/a254647_2.pdf"> Pascal’s triangle and recurrence relations for partial sums of m-th powers </a>
%H A254683 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A254683 G.f.: (x + 57*x^2 + 302*x^3 + 302*x^4 + 57*x^5 + x^6)/(- 1 + x)^12.
%F A254683 a(n) = n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(5 + 2*n)*(- 3 + 5*n + n^2)*(4 + 15*n + 3*n^2)/332640.
%F A254683 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + n^6.
%e A254683 First differences: 1, 63, 665, 3367, 11529, ... (A022522)
%e A254683 --------------------------------------------------------------------------
%e A254683 The sixth powers: 1, 64, 729, 4096, 15625, ... (A001014)
%e A254683 --------------------------------------------------------------------------
%e A254683 First partial sums: 1, 65, 794, 4890, 20515, ... (A000540)
%e A254683 Second partial sums: 1, 66, 860, 5750, 26265, ... (A101093)
%e A254683 Third partial sums: 1, 67, 927, 6677, 32942, ... (A254640)
%e A254683 Fourth partial sums: 1, 68, 995, 7672, 40614, ... (A254645)
%e A254683 Fifth partial sums: 1, 69, 1064, 8736, 49350, ... (this sequence)
%t A254683 Table[n (1 + n) (2 + n) (3 + n) (4 + n) (5 + n) (5 + 2*n) (- 3 + 5*n + n^2) (4 + 15 n + 3 n^2)/332640, {n,22}] (* or *)
%t A254683 CoefficientList[Series[(1 + 57 x + 302 x^2 + 302 x^3 + 57 x^4 + x^5)/(- 1 + x)^12, {x,0,21}], x]
%Y A254683 Cf. A000540, A001014, A022522, A101093, A254640, A254645, A254681, A254682, A254684.
%K A254683 nonn,easy
%O A254683 1,2
%A A254683 _Luciano Ancora_, Feb 12 2015