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A341071 Number of compositions of 2n into n squarefree parts.

%I A341071 #14 May 27 2023 02:11:17
%S A341071 1,1,3,7,23,76,267,932,3263,11410,40028,140955,498467,1769249,6299282,
%T A341071 22485487,80435919,288275461,1034862558,3720499175,13393720428,
%U A341071 48275699654,174194970601,629187941167,2274710068067,8230764250326,29805342037721,108009638665648
%N A341071 Number of compositions of 2n into n squarefree parts.
%H A341071 Alois P. Heinz, <a href="/A341071/b341071.txt">Table of n, a(n) for n = 0..1000</a>
%F A341071 a(n) ~ c * d^n / sqrt(n), where d = 3.6921332109291502908930783402282652076342401140592914... and c = 0.27220098720735952890181498005903942865018992276116... - _Vaclav Kotesovec_, Feb 14 2021
%p A341071 b:= proc(n, t) option remember;
%p A341071       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341071       `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
%p A341071     end:
%p A341071 a:= n-> b(2*n, n):
%p A341071 seq(a(n), n=0..35);
%t A341071 b[n_, t_] := b[n, t] =
%t A341071   If[n == 0, If[t == 0, 1, 0], If[t < 1, 0, Sum[
%t A341071   If[SquareFreeQ[j], b[n - j, t - 1], 0], {j, 1, n}]]];
%t A341071 a[n_] := b[2n, n];
%t A341071 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, May 26 2023, from Maple program *)
%Y A341071 Cf. A005117, A333047, A338464, A338465, A341072.
%K A341071 nonn
%O A341071 0,3
%A A341071 _Alois P. Heinz_, Feb 04 2021