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A370368 Total sum over all j in [n] of the number of partitions of [j*(n-j)] into (n-j) sets of size j having no set of consecutive numbers whose maximum (if j>0) is a multiple of j.

%I A370368 #13 Feb 18 2024 09:10:10
%S A370368 1,1,1,1,3,18,347,20679,4064088,3206794270,9817417580226,
%T A370368 147957639234186793,9515125170594095021483,
%U A370368 3369265619091187775505912588,5792039079391869138256364232105952,55416702792637442337898498177490975722265
%N A370368 Total sum over all j in [n] of the number of partitions of [j*(n-j)] into (n-j) sets of size j having no set of consecutive numbers whose maximum (if j>0) is a multiple of j.
%H A370368 Alois P. Heinz, <a href="/A370368/b370368.txt">Table of n, a(n) for n = 0..54</a>
%H A370368 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A370368 a(n) = Sum_{j=0..n} A370366(j,n-j).
%F A370368 a(n) = A370407(n) - A370365(n).
%p A370368 b:= proc(n, k) `if`(k=0, `if`(n=0, 1, 0), add(
%p A370368       (-1)^(n-j)*binomial(n, j)*(k*j)!/(j!*k!^j), j=0..n))
%p A370368     end:
%p A370368 a:= n-> add(b(j, n-j), j=0..n):
%p A370368 seq(a(n), n=0..15);
%Y A370368 Antidiagonal sums of A370366.
%Y A370368 Cf. A370365, A370407.
%K A370368 nonn
%O A370368 0,5
%A A370368 _Alois P. Heinz_, Feb 16 2024