A370367 Number of partitions of [n^2] into n sets of size n having no set of consecutive numbers whose maximum (if k>n) is a multiple of n.

1, 0, 2, 252, 2604732, 5192229797500, 3708511647508346445685, 1461034020983306348666869275743970, 450538781472323736156501178553451135548626208528, 146413934881756079673947032145931312279368061228255235014292945848

Offset: 0

Author

Alois P. Heinz, Feb 16 2024

Keywords

• nonn

Examples

			a(2) = 2: 13|24, 14|23.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..27
• Wikipedia, Partition of a set

Crossrefs

Main diagonal of A370366.

Cf. A057599, A370364.

Programs

Maple

a:= n-> add((-1)^(n-j)*binomial(n, j)*(n*j)!/(j!*n!^j), j=0..n):
seq(a(n), n=0..10);

Formula

a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(n*j)!/(j!*n!^j).

a(n) = A370366(n,n).

a(n) = A057599(n) - A370364(n).