

A298423


Number of integer partitions of n such that the predecessor of each part is divisible by the number of parts.


8



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
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OFFSET

0,3


COMMENTS

Note that n is automatically divisible by the number of parts.


LINKS

Table of n, a(n) for n=0..71.


FORMULA

G.f.: Sum_{k>=0} x^k/Product_{i=1..k} (1x^(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}]


CROSSREFS

Cf. A000005, A000041, A067538, A143773, A280954, A298422, A298424, A298426.
Sequence in context: A322900 A238791 A007012 * A319810 A325250 A062830
Adjacent sequences: A298420 A298421 A298422 * A298424 A298425 A298426


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jan 19 2018


STATUS

approved



