%I #14 Nov 11 2016 21:49:17

%S 1,0,0,84,210,3696,33264,392964,4879875,66106040,963266304,

%T 15032793048,250055167908,4415595820608,82483140014880,

%U 1624829831302104,33659674920420549,731455984834451184,16636624374027720832

%N Seventh column (k=6) of triangle A134832 (circular succession numbers).

%C a(n) enumerates circular permutations of {1,2,...,n+6} with exactly six successor pairs (i,i+1). Due to cyclicity also (n+6,1) is a successor pair.

%D Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 183, eq. (5.15), for k=6.

%H G. C. Greubel, <a href="/A135804/b135804.txt">Table of n, a(n) for n = 0..444</a>

%F a(n) = binomial(n+6,6)*A000757(n), n>=0.

%F E.g.f.: (d^6/dx^6) (x^6/6!)*(1-log(1-x))/e^x.

%e a(0)=1 because from the 6!/6 = 120 circular permutations of n=6 elements only one, namely (1,2,3,4,5,6), has six successors.

%t f[n_] := (-1)^n + Sum[(-1)^k*n!/((n - k)*k!), {k, 0, n - 1}]; a[n_, n_] = 1; a[n_, 0] := f[n]; a[n_, k_] := a[n, k] = n/k*a[n - 1, k - 1]; Table[a[n, 6], {n, 6, 25}] (* _G. C. Greubel_, Nov 10 2016 *)

%Y Cf. A135803 (column k=5), A135805 (column k=7).

%K nonn,easy

%O 0,4

%A _Wolfdieter Lang_, Jan 21 2008