|
|
A173000
|
|
a(n) = binomial(n + 4, 4)*9^n.
|
|
8
|
|
|
1, 45, 1215, 25515, 459270, 7440174, 111602610, 1578379770, 21308126895, 277005649635, 3490271185401, 42835146366285, 514021756395420, 6049640671423020, 70002984912180660, 798034027998859524, 8977882814987169645, 99812932472504415465, 1097942257197548570115
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Number of n-permutations (n>=4) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 4 u's.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 45*a(n-1)-810*a(n-2)+7290*a(n-3)-32805*a(n-4)+59049*a(n-5). - Wesley Ivan Hurt, Apr 21 2021
Sum_{n>=0} 1/a(n) = 2172 - 18432*log(9/8).
Sum_{n>=0} (-1)^n/a(n) = 36000*log(10/9) - 3792. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Binomial[n + 4, 4]*9^n, {n, 0, 20}]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|