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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.
0
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
0,4
FORMULA
G.f.: -x^2 + Product_{k>=1} (1 + x^(a(k)*k) / (1 - x^k)).
EXAMPLE
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].
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 28 2020
STATUS
approved