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A298423
Number of integer partitions of n such that the predecessor of each part is divisible by the number of parts.
11
1, 1, 2, 2, 3, 2, 5, 2, 5, 4, 6, 2, 11, 2, 7, 8, 10, 2, 15, 2, 16, 11, 9, 2, 28, 7, 10, 14, 22, 2, 37, 2, 25, 18, 12, 17, 55, 2, 13, 23, 52, 2, 55, 2, 40, 51, 15, 2, 95, 13, 44, 34, 53, 2, 79, 37, 85, 41, 18, 2, 185, 2, 19, 80, 91, 54, 112, 2, 87, 56, 122, 2
OFFSET
0,3
COMMENTS
Note that n is automatically divisible by the number of parts.
FORMULA
G.f.: Sum_{k>=0} x^k/Product_{i=1..k} (1-x^(k*i)).
EXAMPLE
The a(9) = 4 partitions: (9), (441), (711), (111111111).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Function[ptn, And@@(Divisible[#-1, Length[ptn]]&/@ptn)]]], {n, 60}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 19 2018
STATUS
approved