A298423 Number of integer partitions of n such that the predecessor of each part is divisible by the number of parts.

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.

Links

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

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}]

Crossrefs

Cf. A000005, A000041, A067538, A143773, A280954, A298422, A298424, A298426.

Sequence in context: A238791 A007012 A343371 * A319810 A325250 A062830

Adjacent sequences: A298420 A298421 A298422 * A298424 A298425 A298426

Keyword

nonn

Author

Gus Wiseman, Jan 19 2018

Status

approved