A370364 Number of partitions of [n^2] into n sets of size n having at least one set of consecutive numbers whose maximum (if n>0) is a multiple of n.

0, 1, 1, 28, 22893, 2443061876, 68542265471953355, 833412961429901104030214430, 6514551431426932053792271970458170132097, 45458343253887079540702419310885199704811913950207054152, 375236832464739513549091449370258959406125572044428827214970469920572831639

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..27

Wikipedia, Partition of a set

Formula

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

a(n) = A370363(n,n).

a(n) = A057599(n) - A370367(n).

Example

a(1) = 1: 1.
a(2) = 1: 12|34.
a(3) = 28: 123|456|789, 123|457|689, 123|458|679, 123|459|678, 123|467|589, 123|468|579, 123|469|578, 123|478|569, 123|479|568, 123|489|567, 124|356|789, 125|346|789, 126|345|789, 127|389|456, 128|379|456, 129|378|456, 134|256|789, 135|246|789, 136|245|789, 137|289|456, 138|279|456, 139|278|456, 145|236|789, 146|235|789, 156|234|789, 178|239|456, 179|238|456, 189|237|456.

Maple

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

Crossrefs

Main diagonal of A370363.

Cf. A057599, A370367.

Sequence in context: A280283 A221928 A281324 * A159439 A270070 A159443

Adjacent sequences: A370361 A370362 A370363 * A370365 A370366 A370367

Keyword

nonn

Author

Alois P. Heinz, Feb 16 2024

Status

approved