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%I #15 Jun 11 2022 16:09:15
%S 0,1,3,54,250,1950,10206,64288,350064,2065500,11509300,66905256,
%T 380767608,2226036904,12949377000,76842172800,457297336576,
%U 2766381692688,16849247813424,104116268476000,649043824951200
%N Sum of the numerators for computing the fourth moment of the probability mass function for the number of involutions with k 2-cycles in n elements (A000085) assuming equal likelihood.
%C Since the PMF represents a probability function, there is no unique set of numerators. That is, only the relative magnitude of the sum of the numerators matter so long as the denominator is of the same relative magnitude (since the relative magnitudes cancel upon division).
%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^4*n!/((n-2*k)!*2^k*k!).
%o (PARI) a(n) = sum(k=0, n\2 ,k^4*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 More data from _Michel Marcus_, Aug 10 2013