A339246 - OEIS

%I #6 Nov 28 2020 20:04:22

%S 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 110,122,140,154,178,195,223,245,276,303,344,376,421,461,513,561,627,

%U 681,756,824,909,988,1092,1182,1301,1413,1547,1673,1834,1979,2165,2341,2548,2746,2993

%N 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 <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: -x^2 + Product_{k>=1} (1 + x^(a(k)*k) / (1 - x^k)).

%e a(0) = a(1) = a(2) = 1: by definition.

%e a(3) = 2: [2, 1], [1, 1, 1].

%e a(4) = 3: [2, 2], [2, 1, 1], [1, 1, 1, 1].

%e a(5) = 3: [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1].

%e a(6) = 5: [3, 3], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1].

%Y Cf. A115584, A117144, A151945.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Nov 28 2020