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 A284942 #17 Aug 07 2019 17:28:20
%S A284942 1,3,8,19,46,107,244,547,1213,2665,5807,12567,27042,57899,123428,
%T A284942 262115,554750,1170538,2463154,5170462,10829234,22635087,47223412,
%U A284942 98353299,204519549,424665001,880581806,1823667221,3772341661,7794697759,16089424392,33178906531,68357928558
%N A284942 Expansion of Sum_{k>=1} mu(k)^2*x^k*(1 - x)^2/(1 - 2*x)^2, where mu() is the Moebius function (A008683).
%C A284942 Total number of squarefree parts in all compositions (ordered partitions) of n.
%H A284942 Alois P. Heinz, <a href="/A284942/b284942.txt">Table of n, a(n) for n = 1..3312</a>
%H A284942 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A284942 G.f.: Sum_{k>=1} mu(k)^2*x^k*(1 - x)^2/(1 - 2*x)^2.
%e A284942 a(4) = 19 because we have [4], [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1] and 0 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 19.
%p A284942 a:= proc(n) option remember; add(`if`(numtheory[
%p A284942 issqrfree](j), ceil(2^(n-j-1)), 0)+a(n-j), j=1..n)
%p A284942 end:
%p A284942 seq(a(n), n=1..33); # _Alois P. Heinz_, Aug 07 2019
%t A284942 nmax = 33; Rest[CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k (1 - x)^2/(1 - 2 x)^2, {k, 1, nmax}], {x, 0, nmax}], x]]
%o A284942 (PARI) x='x+O('x^34); Vec(sum(k=1, 34, moebius(k) ^2*x^k*(1 - x)^2/(1 - 2*x)^2)) \\ _Indranil Ghosh_, Apr 06 2017
%Y A284942 Cf. A005117, A008683, A011782, A059570, A097941, A097979, A102291, A281573, A284943.
%K A284942 nonn
%O A284942 1,2
%A A284942 _Ilya Gutkovskiy_, Apr 06 2017