A324357 Total number of occurrences of 7 in the (signed) displacement sets of all permutations of [n+7] divided by 7!.

0, 1, 15, 193, 2479, 33081, 464807, 6906257, 108589887, 1805179321, 31676392519, 585609896433, 11383428770303, 232204651095353, 4961029124266599, 110811507291845521, 2583228239189752447, 62748345739947178617, 1585780756628964990407, 41635723030339339863281

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..444

Wikipedia, Permutation

Formula

E.g.f.: (1-exp(-x))/(1-x)^8.

a(n) = -1/7! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+7-j)!.

a(n) = A306234(n+7,7).

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(7):
seq(a(n), n=0..23);

Crossrefs

Column k=7 of A324362.

Cf. A306234.

Sequence in context: A220528 A006238 A201883 * A172204 A015673 A377261

Adjacent sequences: A324354 A324355 A324356 * A324358 A324359 A324360

Keyword

nonn

Author

Alois P. Heinz, Feb 23 2019

Status

approved