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.
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, 110, 122, 140, 154, 178, 195, 223, 245, 276, 303, 344, 376, 421, 461, 513, 561, 627, 681, 756, 824, 909, 988, 1092, 1182, 1301, 1413, 1547, 1673, 1834, 1979, 2165, 2341, 2548, 2746, 2993
Offset: 0
Keywords
Examples
a(0) = a(1) = a(2) = 1: by definition. a(3) = 2: [2, 1], [1, 1, 1]. a(4) = 3: [2, 2], [2, 1, 1], [1, 1, 1, 1]. a(5) = 3: [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]. a(6) = 5: [3, 3], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1].
Formula
G.f.: -x^2 + Product_{k>=1} (1 + x^(a(k)*k) / (1 - x^k)).