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

1, 2, 3, 4, 7, 29, 424, 22250, 4166012, 3228619112, 9836415861419, 148021077093705105, 9516162824804128833773, 3369338041967340627557507931, 5792066385997100947453116161699033, 55416753515944143275546728017602371379095

Offset: 0

Author

Alois P. Heinz, Feb 17 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..54

Crossrefs

Cf. A060540, A275973, A361948, A370365, A370368.

Programs

Maple

a:= n-> add(`if`(j=n, 1, (j*(n-j))!/((n-j)!^j*j!)), j=0..n):
seq(a(n), n=0..15);

Formula

a(n) = A370365(n) + A370368(n).

a(n) = Sum_{j=0..n} A361948(j,n-j).

a(n) mod 2 = A275973(n-1) for n>=2.