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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..55

Wikipedia, Partition of a set

Formula

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

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

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);

Crossrefs

Antidiagonal sums of A370363.

Cf. A370368, A370407.

Sequence in context: A116054 A339782 A176621 * A099527 A354371 A345276

Adjacent sequences: A370362 A370363 A370364 * A370366 A370367 A370368

Keyword

nonn

Author

Alois P. Heinz, Feb 16 2024

Status

approved