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, 1, 3, 54, 250, 1950, 10206, 64288, 350064, 2065500, 11509300, 66905256, 380767608, 2226036904, 12949377000, 76842172800, 457297336576, 2766381692688, 16849247813424, 104116268476000, 649043824951200

Offset: 1

Author

Rajan Murthy, Nov 30 2010

Keywords

• nonn

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

Crossrefs

First moment numerators are given by A162970. The denominator is given by A000085.

Programs

PARI

a(n) = sum(k=0, n\2 ,k^4*n!/((n-2*k)!*2^k*k!)); \\ Michel Marcus, Aug 10 2013

Formula

a(n)=Sum_{k=0..[ n/2 ]} k^4*n!/((n-2*k)!*2^k*k!).

Extensions

More data from Michel Marcus, Aug 10 2013