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 A369406 #6 Jan 22 2024 23:59:35
%S A369406 1,2,3,4,5,6,7,8,10,19,56,177,508,1301,3018,6451,12887,24328,43777,
%T A369406 75602,125991,203512,319793,490338,735496,1081601,1562302,2220104,
%U A369406 3108162,4292581,5857016,7920222,10719709,14991758,23535855,47071676,124403657,386938194,1252225819
%N A369406 a(n) = Sum_{k=0..n} binomial(n,k^3).
%C A369406 a(n) equals the number of subsets of [n] whose cardinalities are cube.
%C A369406 Binomial transform of the characteristic function of cubes A010057.
%C A369406 Partial sums of A280351.
%F A369406 G.f.: (1/(1 - x)) * Sum_{k>=0} (x/(1 - x))^(k^3).
%t A369406 Table[Sum[Binomial[n, k^3], {k, 0, n^(1/3)}], {n, 0, 38}]
%t A369406 nmax = 38; CoefficientList[Series[(1/(1 - x)) Sum[(x/(1 - x))^k^3, {k, 0, nmax}], {x, 0, nmax}], x]
%Y A369406 Cf. A010057, A003099, A280351.
%K A369406 nonn
%O A369406 0,2
%A A369406 _Ilya Gutkovskiy_, Jan 22 2024