A174774 Sum of the numerators for computing the third moment of the probability mass function for probability of k pairs among the involutions on n elements (A000085) assuming equal likelihood.

0, 1, 3, 30, 130, 780, 3696, 19768, 97560, 510660, 2603260, 13754136, 72333768, 390339040, 2116922640, 11722194240, 65521880896, 372897624528, 2146502657520, 12558129505120, 74371827119520, 447090649997376

Offset: 1

Author

Rajan Murthy, Nov 30 2010

Keywords

• nonn

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^3*n!/((n-2*k)!*2^k*k!)); \\ Michel Marcus, Aug 10 2013

Formula

a(n)=Sum_{k=0..[ n/2 ]} k^3*n!/((n-2*k)!*2^k*k!).

Extensions

Corrected, and more terms from Michel Marcus, Aug 10 2013