login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of ordered partitions of an n-set into blocks of size <= n/2.
1

%I #7 Dec 28 2023 10:57:59

%S 1,0,2,6,66,450,4550,45570,543130,7044450,102177222,1621316466,

%T 28089336198,526810157874,10641259374174,230281144233426,

%U 5315651069181882,130370668142722722,3385534486308684710,92801581965119911026,2677687786557636155446,81124824677426691365490

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

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

%F a(n) ~ sqrt(Pi/2) * n^(n + 1/2) / (exp(n) * log(2)^(n+1)). - _Vaclav Kotesovec_, Dec 28 2023

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

%Y Cf. A000670, A368503, A368511.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Dec 28 2023