A200144 The number of multinomial coefficients, based on a set of partitions of n into m positions, divisible by m entirely.

1, 1, 2, 3, 6, 7, 14, 17, 27, 34, 55, 64, 100, 121, 167, 213, 296, 354, 489, 594, 776, 964, 1254, 1511, 1951, 2378, 2986, 3643, 4564, 5483, 6841, 8245, 10099, 12190, 14862, 17783, 21636, 25849, 31184

Offset: 1

Author

Dmitry Kruchinin, Nov 11 2011

Keywords

• nonn

Comments

If n is prime, then the number of multinomial coefficients, based on a set of partitions of n at position m, divided by m entirely, less 1 than the number of partitions of numbers for all m.

Examples

			n=7;
  Set of partitions of n into m=4 parts
[1,1,1,4]
[1,1,2,3]
[1,2,2,2]
number of different parts
[3,1]
[2,1,1]
[1,3]
Multinomial coefficient,  divisible by m
4!/(4*(1!*3!))=1
4!/(4*(2!*1!*1!))=2
4!/(4*(1!*3!))=1
Set of partitions of n into m=7 parts
[1,1,1,1,1,1,1]
number of different parts
[7]
Multinomial coefficient,  divisible by m
7!/(7*(7!))=1/7
		

Links

• Dmitry Kruchinin The number of multinomial coefficients based on a set of partitions of n into k parts and divided by k evenly

Programs

Maxima

/* count number of partitions of n into m parts */
b(n, m):=if n