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