cp's OEIS Frontend

A370407 Total sum over all j in [n] of the number of partitions of [j*(n-j)] into (n-j) sets of size j.

%I A370407 #13 Feb 18 2024 10:43:05
%S A370407 1,2,3,4,7,29,424,22250,4166012,3228619112,9836415861419,
%T A370407 148021077093705105,9516162824804128833773,
%U A370407 3369338041967340627557507931,5792066385997100947453116161699033,55416753515944143275546728017602371379095
%N A370407 Total sum over all j in [n] of the number of partitions of [j*(n-j)] into (n-j) sets of size j.
%H A370407 Alois P. Heinz, <a href="/A370407/b370407.txt">Table of n, a(n) for n = 0..54</a>
%F A370407 a(n) = A370365(n) + A370368(n).
%F A370407 a(n) = Sum_{j=0..n} A361948(j,n-j).
%F A370407 a(n) mod 2 = A275973(n-1) for n>=2.
%p A370407 a:= n-> add(`if`(j=n, 1, (j*(n-j))!/((n-j)!^j*j!)), j=0..n):
%p A370407 seq(a(n), n=0..15);
%Y A370407 Cf. A060540, A275973, A361948, A370365, A370368.
%K A370407 nonn
%O A370407 0,2
%A A370407 _Alois P. Heinz_, Feb 17 2024