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A325620
Number of integer partitions of n whose reciprocal factorial sum is an integer.
7
1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 14, 14, 15, 16, 18, 19, 20, 22, 24, 25, 26, 28, 31, 33, 34, 36, 39, 41, 43, 45, 49, 52, 54, 57, 61, 65, 68, 71, 76, 80, 84, 88, 93, 98, 103, 107, 113
OFFSET
1,4
COMMENTS
The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
EXAMPLE
The initial terms count the following partitions:
1: (1)
2: (1,1)
3: (1,1,1)
4: (2,2)
4: (1,1,1,1)
5: (2,2,1)
5: (1,1,1,1,1)
6: (2,2,1,1)
6: (1,1,1,1,1,1)
7: (2,2,1,1,1)
7: (1,1,1,1,1,1,1)
8: (2,2,2,2)
8: (2,2,1,1,1,1)
8: (1,1,1,1,1,1,1,1)
9: (2,2,2,2,1)
9: (2,2,1,1,1,1,1)
9: (1,1,1,1,1,1,1,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], IntegerQ[Total[1/(#!)]]&]], {n, 30}]
CROSSREFS
Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316856, A325618, A325621, A325622.
Sequence in context: A373535 A025775 A169993 * A270433 A169994 A169995
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 13 2019
STATUS
approved