|
|
A324357
|
|
Total number of occurrences of 7 in the (signed) displacement sets of all permutations of [n+7] divided by 7!.
|
|
3
|
|
|
0, 1, 15, 193, 2479, 33081, 464807, 6906257, 108589887, 1805179321, 31676392519, 585609896433, 11383428770303, 232204651095353, 4961029124266599, 110811507291845521, 2583228239189752447, 62748345739947178617, 1585780756628964990407, 41635723030339339863281
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
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)!.
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|