cp's OEIS Frontend

A200092 The number of ways of putting n labeled items into k labeled boxes so that each box receives at least 3 objects.

%I A200092 #10 Dec 09 2017 19:14:49
%S A200092 1,1,1,1,20,1,70,1,182,1,420,1680,1,912,12600,1,1914,62370,1,3938,
%T A200092 256410,369600,1,8008,949806,4804800,1,16172,3297294,38678640,1,32526,
%U A200092 10966956,248047800,168168000
%N A200092 The number of ways of putting n labeled items into k labeled boxes so that each box receives at least 3 objects.
%C A200092 Equivalently, the number of ordered set partitions of the set [n] into k blocks of size at least three. When the boxes are unlabeled we obtain A059022.
%F A200092 E.g.f. with additional constant 1: 1/(1 - t*(exp(x) - 1 - x - x^2/2!)) = 1 + t*x^3/3! + t*x^4/4! + t*x^5/5! + (t+20*t^2)*x^6/6! + ....
%F A200092 Recurrence relation: T(n+1,k) = k*(T(n,k) + n*(n-1)/2*T(n-2,k-1)). T(n,k) = k!*A059022(n,k).
%e A200092 Table begins
%e A200092   n\k |  1     2       3
%e A200092   ----+-----------------
%e A200092    3  |  1
%e A200092    4  |  1
%e A200092    5  |  1
%e A200092    6  |  1    20
%e A200092    7  |  1    70
%e A200092    8  |  1   182
%e A200092    9  |  1   420    1680
%e A200092   10  |  1   912   12600
%e A200092   11  |  1  1914   62370
%e A200092   ...
%e A200092 T(6,2) = 20: The arrangements of 6 objects into 2 boxes { } and [ ] so that each box contains at least 3 items are {1,2,3}[4,5,6], {1,2,4}[3,5,6], {1,2,5}[3,4,6], {1,2,6}[3,4,5], {1,3,4}[2,5,6], {1,3,5}[2,4,6], {1,3,6}[2,4,5], {1,4,5}[2,3,6], {1,4,6}[2,3,5], {1,5,6}[2,3,4] and the 10 other possibilities where the contents of a pair of boxes are swapped.
%Y A200092 Cf. A019538, A059022, A200091.
%K A200092 nonn,easy,tabf
%O A200092 3,5
%A A200092 _Peter Bala_, Dec 04 2011