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A324358 Total number of occurrences of 8 in the (signed) displacement sets of all permutations of [n+8] divided by 8!. 3
0, 1, 17, 244, 3455, 50356, 766943, 12274858, 206788751, 3666278080, 68339173319, 1337340802942, 27431518405607, 588814390368244, 13204430589422015, 308877966133175746, 7525275697320564383, 190678032594396773128, 5017985343328106906711, 136977444553573371090790 (list; graph; refs; listen; history; text; internal format)
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 A214175

Adjacent sequences:  A324355 A324356 A324357 * A324359 A324360 A324361

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 23 2019

STATUS

approved

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Last modified January 23 19:36 EST 2020. Contains 331175 sequences. (Running on oeis4.)