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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.

LINKS

Table of n, a(n) for n=1..60.

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)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], IntegerQ[1/Total[1/(#!)]]&]], {n, 30}]

CROSSREFS

Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.

Reciprocal factorial sum: A002966, A316854, A316857, A325618, A325620, A325623.

Sequence in context: A194509 A054716 A261641 * A060145 A257806 A035391

Adjacent sequences:  A325619 A325620 A325621 * A325623 A325624 A325625

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 13 2019

STATUS

approved

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Last modified January 28 09:52 EST 2020. Contains 331319 sequences. (Running on oeis4.)