A368511 Number of ordered partitions of an n-set into blocks of size <= sqrt(n).

1, 1, 2, 6, 66, 450, 3690, 35280, 385560, 6717480, 96117000, 1512819000, 25975395600, 483169486800, 9678799930800, 207733600074000, 5243385642495000, 128458209887007000, 3332234177825553000, 91241046790816923000, 2629791992312269785000, 79586945507310941700000

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * [x^n] 1 / (1 - Sum_{1 <= j <= sqrt(n)} x^j / j!).

Mathematica

Table[n! SeriesCoefficient[1/(1 - Sum[x^j/j!, {j, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 21}]

Crossrefs

Cf. A000670, A368502, A368512.

Sequence in context: A066756 A070872 A055685 * A368512 A262047 A280393

Adjacent sequences: A368508 A368509 A368510 * A368512 A368513 A368514

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 28 2023

Status

approved