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Number of connected groupoids (categories all of whose morphisms are invertible) with n more morphisms than objects.
2

%I #2 Mar 31 2012 10:31:22

%S 2,1,2,2,1,2,3,5,2,2,2,5,2,2,3,15,1,5,2,5,3,2,3,15,3,2,6,4,2,4,7,51,1,

%T 4,3,14,1,2,4,14,1,6,4,4,3,3,6,52,2,5,2,7,1,15,4,13,3,2,2,13,4,2,18,

%U 267,1,4,3,5,1,9,7,50,2,2,4,4,2,6,8,52,15,2,3,15,1,2,3,14,1,10,3,5,4

%N Number of connected groupoids (categories all of whose morphisms are invertible) with n more morphisms than objects.

%C a(n) >= A000001(n+1) (number of groups of order n+1).

%F a(0) = 2 and if n>0, a(n) = sum(A000001((n+k)/(k^2)),k^2|n+k). (see formula for A140185)

%Y Cf. A140185, A140187, A140188.

%K nonn

%O 0,1

%A _Benoit Jubin_, May 12 2008