A135804 Seventh column (k=6) of triangle A134832 (circular succession numbers).

1, 0, 0, 84, 210, 3696, 33264, 392964, 4879875, 66106040, 963266304, 15032793048, 250055167908, 4415595820608, 82483140014880, 1624829831302104, 33659674920420549, 731455984834451184, 16636624374027720832

Offset

0,4

Comments

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.

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..444

Formula

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

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

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A072589 A181113 A254464 * A211256 A335081 A219808

Adjacent sequences: A135801 A135802 A135803 * A135805 A135806 A135807

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 21 2008

Status

approved