This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A174782 #15 Jun 11 2022 16:09:15
%S A174782 0,1,3,54,250,1950,10206,64288,350064,2065500,11509300,66905256,
%T A174782 380767608,2226036904,12949377000,76842172800,457297336576,
%U A174782 2766381692688,16849247813424,104116268476000,649043824951200
%N A174782 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 A174782 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 A174782 Wikipedia, <a href="http://en.wikipedia.org/wiki/Probability_mass_function">Probability Mass Function</a>
%F A174782 a(n)=Sum_{k=0..[ n/2 ]} k^4*n!/((n-2*k)!*2^k*k!).
%o A174782 (PARI) a(n) = sum(k=0, n\2 ,k^4*n!/((n-2*k)!*2^k*k!)); \\ _Michel Marcus_, Aug 10 2013
%Y A174782 First moment numerators are given by A162970. The denominator is given by A000085.
%K A174782 nonn
%O A174782 1,3
%A A174782 _Rajan Murthy_, Nov 30 2010
%E A174782 More data from _Michel Marcus_, Aug 10 2013