A370368 - OEIS

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 #13 Feb 18 2024 09:10:10

%S 1,1,1,1,3,18,347,20679,4064088,3206794270,9817417580226,

%T 147957639234186793,9515125170594095021483,

%U 3369265619091187775505912588,5792039079391869138256364232105952,55416702792637442337898498177490975722265

%N 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 Alois P. Heinz, <a href="/A370368/b370368.txt">Table of n, a(n) for n = 0..54</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} A370366(j,n-j).

%F a(n) = A370407(n) - A370365(n).

%p b:= proc(n, k) `if`(k=0, `if`(n=0, 1, 0), add(

%p (-1)^(n-j)*binomial(n, j)*(k*j)!/(j!*k!^j), j=0..n))

%p end:

%p a:= n-> add(b(j, n-j), j=0..n):

%p seq(a(n), n=0..15);

%Y Antidiagonal sums of A370366.

%Y Cf. A370365, A370407.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Feb 16 2024