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A341069 Number of ways to write n as an ordered sum of 9 squarefree numbers.

%I A341069 #6 Feb 04 2021 17:30:24
%S A341069 1,9,45,156,423,963,1959,3708,6669,11410,18594,29052,44046,65196,
%T A341069 94284,133104,184248,251406,338995,450936,591885,768657,990567,
%U A341069 1265832,1602273,2010294,2506572,3107136,3825675,4676643,5686347,6882912,8290431,9928305,11834289,14052816,16624846
%N A341069 Number of ways to write n as an ordered sum of 9 squarefree numbers.
%F A341069 G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^9.
%p A341069 b:= proc(n, t) option remember;
%p A341069       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341069       `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
%p A341069     end:
%p A341069 a:= n-> b(n, 9):
%p A341069 seq(a(n), n=9..45);  # _Alois P. Heinz_, Feb 04 2021
%t A341069 nmax = 45; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &
%Y A341069 Cf. A005117, A008683, A008966, A098235, A280210, A326522, A341064, A341065, A341066, A341067, A341068, A341070.
%K A341069 nonn
%O A341069 9,2
%A A341069 _Ilya Gutkovskiy_, Feb 04 2021