A324358 Total number of occurrences of 8 in the (signed) displacement sets of all permutations of [n+8] divided by 8!.

0, 1, 17, 244, 3455, 50356, 766943, 12274858, 206788751, 3666278080, 68339173319, 1337340802942, 27431518405607, 588814390368244, 13204430589422015, 308877966133175746, 7525275697320564383, 190678032594396773128, 5017985343328106906711, 136977444553573371090790

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..443

Wikipedia, Permutation

Formula

E.g.f.: (1-exp(-x))/(1-x)^9.

a(n) = -1/8! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+8-j)!.

a(n) = A306234(n+8,8).

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(8):
seq(a(n), n=0..23);

Crossrefs

Column k=8 of A324362.

Cf. A306234.

Sequence in context: A196987 A051560 A259347 * A294608 A294810 A362233

Adjacent sequences: A324355 A324356 A324357 * A324359 A324360 A324361

Keyword

nonn

Author

Alois P. Heinz, Feb 23 2019

Status

approved