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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..444
- Wikipedia, Permutation
Programs
-
Maple
a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(7): seq(a(n), n=0..23);
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).