|
|
A309184
|
|
(1/5) times the number of n-member subsets of [5n] whose elements sum to a multiple of n.
|
|
2
|
|
|
1, 4, 31, 244, 2126, 19780, 192130, 1922740, 19692535, 205444504, 2175519380, 23322657460, 252631900236, 2760767859784, 30400169157656, 336977765092788, 3757141504436393, 42107201575818028, 474084628585822413, 5359833704140818744, 60823006052351729266
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Also (1/4) times the number of n-member subsets of [5n-1] whose elements sum to a multiple of n.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 1/(5n) * Sum_{d|n} binomial(5d,d)*(-1)^(n+d)*phi(n/d).
|
|
MAPLE
|
with(numtheory):
a:= n-> add(binomial(5*d, d)*(-1)^(n+d)*
phi(n/d), d in divisors(n))/(5*n):
seq(a(n), n=1..25);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|