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A325622
Number of integer partitions of n whose reciprocal factorial sum is the reciprocal of an integer.
7
1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 3, 3, 2, 2, 3, 3, 3, 5, 4, 4, 3, 3, 4, 6, 3, 4, 5, 5, 5, 6, 3, 7, 6, 5, 6, 6, 6, 5, 6, 8, 5, 7, 5, 4, 8, 7, 7, 7, 7, 9, 9, 9, 10, 12, 6, 12, 8, 10, 7, 14, 10, 8, 11, 11, 12, 11, 10, 10, 12, 14
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: (2)
3: (3)
4: (4)
4: (2,2)
5: (5)
6: (6)
6: (3,3)
7: (7)
8: (8)
8: (4,4)
9: (9)
9: (5,4)
9: (3,3,3)
10: (10)
10: (5,5)
11: (11)
11: (4,4,3)
11: (3,3,3,2)
12: (12)
12: (6,6)
12: (4,4,4)
MAPLE
f:= proc(n) nops(select(proc(t) local i; (1/add(1/i!, i=t))::integer end proc, combinat:-partition(n))) end proc:
map(f, [$1..70]); # Robert Israel, May 09 2024
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], IntegerQ[1/Total[1/(#!)]]&]], {n, 30}]
CROSSREFS
Reciprocal factorial sum: A002966, A316854, A316857, A325618, A325620, A325623.
Sequence in context: A194509 A054716 A261641 * A060145 A358997 A373461
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 13 2019
EXTENSIONS
a(61)-a(70) from Robert Israel, May 09 2024
STATUS
approved