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 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. 0
 0, 1, 3, 54, 250, 1950, 10206, 64288, 350064, 2065500, 11509300, 66905256, 380767608, 2226036904, 12949377000, 76842172800, 457297336576, 2766381692688, 16849247813424, 104116268476000, 649043824951200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). LINKS Wikipedia, Probability Mass Function FORMULA a(n)=Sum_{k=0..[ n/2 ]} k^4*n!/((n-2*k)!*2^k*k!). PROG (PARI) a(n) = sum(k=0, n\2 , k^4*n!/((n-2*k)!*2^k*k!)); \\ Michel Marcus, Aug 10 2013 CROSSREFS First moment numerators are given by A162970. The denominator is given by A000085. Sequence in context: A045481 A275566 A068380 * A345074 A119294 A157541 Adjacent sequences: A174779 A174780 A174781 * A174783 A174784 A174785 KEYWORD nonn AUTHOR Rajan Murthy, Nov 30 2010 EXTENSIONS More data from Michel Marcus, Aug 10 2013 STATUS approved

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Last modified March 31 21:40 EDT 2023. Contains 361673 sequences. (Running on oeis4.)