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A339246 a(n) = 1 for n <= 2; thereafter a(n) is the number of partitions of n where every part k appears at least a(k) times.

%I A339246 #6 Nov 28 2020 20:04:22
%S A339246 1,1,1,2,3,3,5,5,7,8,10,11,15,16,20,23,28,31,38,41,50,56,66,72,86,94,
%T A339246 110,122,140,154,178,195,223,245,276,303,344,376,421,461,513,561,627,
%U A339246 681,756,824,909,988,1092,1182,1301,1413,1547,1673,1834,1979,2165,2341,2548,2746,2993
%N A339246 a(n) = 1 for n <= 2; thereafter a(n) is the number of partitions of n where every part k appears at least a(k) times.
%H A339246 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A339246 G.f.: -x^2 + Product_{k>=1} (1 + x^(a(k)*k) / (1 - x^k)).
%e A339246 a(0) = a(1) = a(2) = 1: by definition.
%e A339246 a(3) = 2: [2, 1], [1, 1, 1].
%e A339246 a(4) = 3: [2, 2], [2, 1, 1], [1, 1, 1, 1].
%e A339246 a(5) = 3: [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1].
%e A339246 a(6) = 5: [3, 3], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1].
%Y A339246 Cf. A115584, A117144, A151945.
%K A339246 nonn
%O A339246 0,4
%A A339246 _Ilya Gutkovskiy_, Nov 28 2020