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%I #9 Feb 24 2022 07:25:29
%S 1,1,1,1,3,2,3,3,7,7,8,10,16,18,18,22,33,35,39,47,65,69,77,89,117,126,
%T 138,163,205,223,242,282,344,376,407,466,561,612,664,751,889,966,1047,
%U 1176,1365,1488,1606,1792,2056,2240,2406,2672,3032,3286,3532,3891
%N Number of partitions of n into 9 distinct squarefree parts.
%p b:= proc(n, i, t) option remember; `if`(n=0,
%p `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
%p end:
%p a:= n-> b(n$2, 9):
%p seq(a(n), n=58..113); # _Alois P. Heinz_, Feb 04 2021
%t b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t a[n_] := b[n, n, 9];
%t Table[a[n], {n, 58, 113}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y Cf. A005117, A008966, A098236, A307835, A326522, A341069, A341073, A341074, A341075, A341095, A341096, A341098.
%K nonn
%O 58,5
%A _Ilya Gutkovskiy_, Feb 04 2021
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