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%I A370367 #13 Feb 17 2024 17:41:20
%S A370367 1,0,2,252,2604732,5192229797500,3708511647508346445685,
%T A370367 1461034020983306348666869275743970,
%U A370367 450538781472323736156501178553451135548626208528,146413934881756079673947032145931312279368061228255235014292945848
%N 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.
%H A370367 Alois P. Heinz, <a href="/A370367/b370367.txt">Table of n, a(n) for n = 0..27</a>
%H A370367 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A370367 a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(n*j)!/(j!*n!^j).
%F A370367 a(n) = A370366(n,n).
%F A370367 a(n) = A057599(n) - A370364(n).
%e A370367 a(2) = 2: 13|24, 14|23.
%p A370367 a:= n-> add((-1)^(n-j)*binomial(n, j)*(n*j)!/(j!*n!^j), j=0..n):
%p A370367 seq(a(n), n=0..10);
%Y A370367 Main diagonal of A370366.
%Y A370367 Cf. A057599, A370364.
%K A370367 nonn
%O A370367 0,3
%A A370367 _Alois P. Heinz_, Feb 16 2024

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