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%I #10 Apr 30 2012 10:45:38
%S 1,2,4,15,72,472,3448,29264,273371,2834368,31998904,392958758,
%T 5201061456,73955306224,1123596636018,18177574748625,311951144828864,
%U 5661773589217182,108355864447215064,2181104926663522206,46066653269313449442,1018706122380363766288
%N The number of n-permutations whose connected components have the same size.
%C See A003319 for definition of connected component.
%C a(p) = A003319(p)+1 for all prime numbers, p.
%F O.g.f.: Sum_{n>0} 1/(1-A003319(n)*x^n).
%e a(4) = 15 because there are 13 connected permutations of {1,2,3,4} (these are counted by A003319) and 21/43 and 1/2/3/4.
%t nn = 20; p = Sum[n! x^n, {n, 0, nn}]; i = 1 - 1/p; a = CoefficientList[Series[i, {x, 0, nn}], x]; s = Sum[1/(1 - a[[n + 1]] x^n), {n, 1, nn}]; Drop[ CoefficientList[Series[s, {x, 0, nn}], x], 1]
%K nonn
%O 1,2
%A _Geoffrey Critzer_, Apr 29 2012
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