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

1,3

Links

Table of n, a(n) for n=1..22.

Wikipedia, Probability Mass Function

Formula

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

Prog

(PARI) a(n) = sum(k=0, n\2 , k^3*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: A225018 A365290 A221516 * A020874 A161806 A003689

Adjacent sequences: A174771 A174772 A174773 * A174775 A174776 A174777

Keyword

nonn

Author

Rajan Murthy, Nov 30 2010

Extensions

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

Status

approved