A370367 - OEIS

%I #13 Feb 17 2024 17:41:20

%S 1,0,2,252,2604732,5192229797500,3708511647508346445685,

%T 1461034020983306348666869275743970,

%U 450538781472323736156501178553451135548626208528,146413934881756079673947032145931312279368061228255235014292945848

%N 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.

%H Alois P. Heinz, <a href="/A370367/b370367.txt">Table of n, a(n) for n = 0..27</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

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

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

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

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

%p a:= n-> add((-1)^(n-j)*binomial(n, j)*(n*j)!/(j!*n!^j), j=0..n):

%p seq(a(n), n=0..10);

%Y Main diagonal of A370366.

%Y Cf. A057599, A370364.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 16 2024