login
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
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).
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
KEYWORD
nonn
AUTHOR
Rajan Murthy, Nov 30 2010
EXTENSIONS
More data from Michel Marcus, Aug 10 2013
STATUS
approved