login
A368511
Number of ordered partitions of an n-set into blocks of size <= sqrt(n).
1
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 28 2023
STATUS
approved