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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.
4
0, 1, 2, 3, 4, 11, 77, 1571, 101924, 21824842, 18998281193, 63437859518312, 1037654210033812290, 72422876152852051595343, 27306605231809196751929593081, 50723306700937648229840111395656830, 510196838745355443955126736574361550469276
OFFSET
0,3
LINKS
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.
Sequence in context: A116054 A339782 A176621 * A099527 A354371 A345276
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 16 2024
STATUS
approved