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A341098 Number of partitions of n into 10 distinct squarefree parts.

%I A341098 #8 Feb 24 2022 07:16:58
%S A341098 1,1,1,1,2,3,2,4,6,8,7,10,14,17,17,22,32,35,37,47,62,71,72,91,114,132,
%T A341098 136,167,205,234,247,293,355,398,426,497,590,661,708,819,956,1066,
%U A341098 1141,1306,1501,1672,1791,2030,2318,2559,2747,3081,3490,3835,4115
%N A341098 Number of partitions of n into 10 distinct squarefree parts.
%p A341098 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341098       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341098       `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341098     end:
%p A341098 a:= n-> b(n$2, 10):
%p A341098 seq(a(n), n=72..126);  # _Alois P. Heinz_, Feb 04 2021
%t A341098 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341098      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341098      If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341098 a[n_] := b[n, n, 10];
%t A341098 Table[a[n], {n, 72, 126}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y A341098 Cf. A005117, A008966, A098236, A307835, A326626, A341070, A341073, A341074, A341075, A341095, A341096, A341097.
%K A341098 nonn
%O A341098 72,5
%A A341098 _Ilya Gutkovskiy_, Feb 04 2021