A368502 Number of partitions of an n-set into blocks of size <= sqrt(n).

1, 1, 1, 1, 10, 26, 76, 232, 764, 12644, 61136, 312676, 1680592, 9467680, 55704104, 341185496, 6631556521, 49294051497, 380306658250, 3039453750685, 25120541332271, 214363100120051, 1885987611214092, 17085579637664715, 159185637725413675, 3282701194678476257

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2023

Keywords

• nonn

Crossrefs

Cf. A000110, A097356, A368503.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[Sum[x^j/j!, {j, 1, Floor[Sqrt[n]]}]], {x, 0, n}], {n, 0, 25}]

Formula

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