A324358 - OEIS

%I #7 Feb 24 2019 15:06:30

%S 0,1,17,244,3455,50356,766943,12274858,206788751,3666278080,

%T 68339173319,1337340802942,27431518405607,588814390368244,

%U 13204430589422015,308877966133175746,7525275697320564383,190678032594396773128,5017985343328106906711,136977444553573371090790

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

%H Alois P. Heinz, <a href="/A324358/b324358.txt">Table of n, a(n) for n = 0..443</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

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

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

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

%p a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(8):

%p seq(a(n), n=0..23);

%Y Column k=8 of A324362.

%Y Cf. A306234.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 23 2019