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

%I #5 Dec 27 2023 22:37:27

%S 1,0,1,1,10,26,166,652,3795,18755,112124,648649,4163743,27216840,

%T 190168577,1376119903,10468226150,82744297014,681863474058,

%U 5830425411936,51720008131148,474821737584174,4506628734688128,44150936144057758,445956917001833090,4638564968368158592

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

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

%t Table[n! SeriesCoefficient[Exp[Sum[x^j/j!, {j, 1, Floor[n/2]}]], {x, 0, n}], {n, 0, 25}]

%Y Cf. A000110, A110618, A368502.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Dec 27 2023