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 A293550 #8 Apr 07 2018 05:28:08
%S A293550 0,1,11,69,354,1650,7293,31213,130832,540702,2212550,8989090,36327810,
%T A293550 146228940,586823265,2349424125,9389012160,37467344310,149345215290,
%U A293550 594753416790,2366845396500,9413555798556,37423053793026,148719333293394,590842248405024,2346813893147500
%N A293550 a(n) = Sum_{k=0..n} k^3*binomial(2*n-k,n).
%C A293550 Main diagonal of iterated partial sums array of cubes (starting with the first partial sums). For nonnegative integers see A002054, for squares see A265612.
%H A293550 Seiichi Manyama, <a href="/A293550/b293550.txt">Table of n, a(n) for n = 0..1000</a>
%H A293550 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A293550 a(n) = [x^n] x*(1 + 4*x + x^2)/(1 - x)^(n+5).
%F A293550 a(n) = 2^(2*n+1)*n^2*(13*n + 7)*Gamma(n+3/2)/(sqrt(Pi)*Gamma(n+5)).
%F A293550 a(n) ~ 26*4^n/sqrt(Pi*n).
%t A293550 Table[Sum[k^3 Binomial[2 n - k, n], {k, 0, n}], {n, 0, 25}]
%t A293550 Table[SeriesCoefficient[x (1 + 4 x + x^2)/(1 - x)^(n + 5), {x, 0, n}], {n, 0, 25}]
%t A293550 Table[2^(2 n + 1) n^2 (13 n + 7) Gamma[n + 3/2]/(Sqrt[Pi] Gamma[n + 5]), {n, 0, 25}]
%t A293550 CoefficientList[Series[(6 - 6 Sqrt[1 - 4 x] - 36 x + 24 Sqrt[1 - 4 x] x + 55 x^2 - 19 Sqrt[1 - 4 x] x^2 - 15 x^3 + Sqrt[1 - 4 x] x^3)/(2 Sqrt[1 - 4 x] x^4), {x, 0, 25}], x]
%t A293550 CoefficientList[Series[(E^(2 x) (36 - 24 x + 13 x^2) BesselI[0, 2 x])/x^2 + (E^(2 x) (-36 + 24 x - 31 x^2 + 13 x^3) BesselI[1, 2 x])/x^3, {x, 0, 25}], x]* Range[0, 25]!
%Y A293550 Cf. A000537, A000578, A002054, A024166, A101094, A101097, A101102, A265612, A302352.
%K A293550 nonn
%O A293550 0,3
%A A293550 _Ilya Gutkovskiy_, Oct 11 2017