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

1,3

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

Table of n, a(n) for n=1..21.

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