A134515 - OEIS

%I #17 Aug 21 2017 03:11:37

%S 1,0,0,10,15,168,1008,8244,73125,726440,7939008,94744494,1225760627,

%T 17088219120,255365758560,4072255216296,69021889788969,

%U 1239055874931312,23484788783212480,468656477004105810,9821896865573503095

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

%C 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.

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

%H Bhadrachalam Chitturi and Krishnaveni K S, <a href="https://arxiv.org/abs/1601.04469">Adjacencies in Permutations</a>, arXiv preprint arXiv:1601.04469 [cs.DM], 2016.

%F E.g.f.: (d^2/dx^2) (x^2/2!)*(1-log(1-x))/e^x.

%F a(n) = (((n+2)*(n+1))/2)*A000757(n), n>=0.

%e 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.

%Y Cf. A135799 (column k=1).

%K nonn,easy

%O 0,4

%A _Wolfdieter Lang_, Jan 21 2008, Feb 22 2008