A370365 Total sum over all j in [n] of the number of partitions of [j*(n-j)] into (n-j) sets of size j having at least one set of consecutive numbers whose maximum (if j>0) is a multiple of j.

0, 1, 2, 3, 4, 11, 77, 1571, 101924, 21824842, 18998281193, 63437859518312, 1037654210033812290, 72422876152852051595343, 27306605231809196751929593081, 50723306700937648229840111395656830, 510196838745355443955126736574361550469276

Offset: 0

Author

Alois P. Heinz, Feb 16 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..55
• Wikipedia, Partition of a set

Crossrefs

Antidiagonal sums of A370363.

Cf. A370368, A370407.

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0, signum(n), add(
      (-1)^(n-j+1)*binomial(n, j)*(k*j)!/(j!*k!^j), j=0..n-1))
    end:
a:= n-> add(b(j, n-j), j=0..n):
seq(a(n), n=0..16);

Formula

a(n) = Sum_{j=0..n} A370363(j,n-j).

a(n) = A370407(n) - A370368(n).