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

Author

Gus Wiseman, Jan 19 2018

Keywords

• nonn

Comments

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

Examples

			The a(9) = 4 partitions: (9), (441), (711), (111111111).
		

Crossrefs

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

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],Function[ptn,And@@(Divisible[#-1,Length[ptn]]&/@ptn)]]],{n,60}]

Formula

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