A368512 Number of ordered partitions of an n-set into blocks of size <= n/2.

1, 0, 2, 6, 66, 450, 4550, 45570, 543130, 7044450, 102177222, 1621316466, 28089336198, 526810157874, 10641259374174, 230281144233426, 5315651069181882, 130370668142722722, 3385534486308684710, 92801581965119911026, 2677687786557636155446, 81124824677426691365490

Offset

0,3

Links

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

Formula

a(n) = n! * [x^n] 1 / (1 - Sum_{1 <= j <= n/2} x^j / j!).

a(n) ~ sqrt(Pi/2) * n^(n + 1/2) / (exp(n) * log(2)^(n+1)). - Vaclav Kotesovec, Dec 28 2023

Mathematica

Table[n! SeriesCoefficient[1/(1 - Sum[x^j/j!, {j, 1, Floor[n/2]}]), {x, 0, n}], {n, 0, 21}]

Crossrefs

Cf. A000670, A368503, A368511.

Sequence in context: A070872 A055685 A368511 * A262047 A280393 A239696

Adjacent sequences: A368509 A368510 A368511 * A368513 A368514 A368515

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 28 2023

Status

approved