seating of people in arbitrary circles of arbitrary sizes

i hope empty circles are not taken into consideration!!? :D

can u tell the answer if u have ?

no .. empty circles are not taken into consideration (atleast 1 person in a circle)

and i dont have the answer.
This was a question our recently concluded technical - interhostel event

I guess Stirling numbers of the first kind is what you need

http://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind

Yes I think the required number should be
\sum_{k=1}^n \left[\begin{array}{c}n \\ k \end{array}\right]

where \left[\begin{array}{c}n \\ k \end{array}\right] denotes the unsigned Stirling number of the first kind which counts the number of permutations of n elements with k disjoint cycles.