

A134515


Third column (k=2) of triangle A134832 (circular succession numbers).


2



1, 0, 0, 10, 15, 168, 1008, 8244, 73125, 726440, 7939008, 94744494, 1225760627, 17088219120, 255365758560, 4072255216296, 69021889788969, 1239055874931312, 23484788783212480, 468656477004105810, 9821896865573503095
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OFFSET

0,4


COMMENTS

a(n) enumerates circular permutations of {1,2,...,n+2} with exactly two successor pairs (i,i+1). Due to cyclicity also (n+2,1) is a successor pair.


REFERENCES

Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 183, eq. (5.15), for k=2.


LINKS



FORMULA

E.g.f.: (d^2/dx^2) (x^2/2!)*(1log(1x))/e^x.
a(n) = (((n+2)*(n+1))/2)*A000757(n), n>=0.


EXAMPLE

a(2)=0 because the 4!/4 = 6 circular permutations of n=4 elements (1,2,3,4), (1,4,3,2), (1,3,4,2),(1,2,4,3), (1,4,2,3) and (1,3,2,4) have 4,0,1,1,1 and 1 successor pair, respectively.


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



