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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
0, 1, 3, 30, 130, 780, 3696, 19768, 97560, 510660, 2603260, 13754136, 72333768, 390339040, 2116922640, 11722194240, 65521880896, 372897624528, 2146502657520, 12558129505120, 74371827119520, 447090649997376 (list; graph; refs; listen; history; text; internal format)
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: A031205 A225018 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

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Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)