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%I #17 Aug 12 2013 02:56:00
%S 0,1,3,30,130,780,3696,19768,97560,510660,2603260,13754136,72333768,
%T 390339040,2116922640,11722194240,65521880896,372897624528,
%U 2146502657520,12558129505120,74371827119520,447090649997376
%N Sum of the numerators for computing the third moment of the probability mass function for probability of k pairs among the involutions on n elements (A000085) assuming equal likelihood.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Probability_mass_function">Probability Mass Function</a>
%F a(n)=Sum_{k=0..[ n/2 ]} k^3*n!/((n-2*k)!*2^k*k!).
%o (PARI) a(n) = sum(k=0, n\2 ,k^3*n!/((n-2*k)!*2^k*k!)); \\ _Michel Marcus_, Aug 10 2013
%Y First moment numerators are given by A162970. The denominator is given by A000085.
%K nonn
%O 1,3
%A _Rajan Murthy_, Nov 30 2010
%E Corrected, and more terms from _Michel Marcus_, Aug 10 2013
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