|
|
A324523
|
|
Number of colored set partitions of [2n] where elements of subsets have distinct colors and exactly n colors are used.
|
|
2
|
|
|
1, 1, 74, 31770, 42687960, 134092967400, 831428629796160, 9095459029214397840, 162061482211484681105280, 4429476877635332233622271360, 177245727799376537644530489120000, 10002691163041098923871227379695673600, 772102922309973700712743861257373871078400
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(n, k) option remember; `if`(n=0, 1, add(k!/(k-j)!
*binomial(n-1, j-1)*b(n-j, k), j=1..min(k, n)))
end:
a:= n-> add(b(2*n, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..15);
|
|
MATHEMATICA
|
b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[k!/(k-j)! Binomial[n - 1, j - 1]* b[n - j, k], {j, 1, Min[k, n]}]];
a[n_] := Sum[b[2n, n - i] (-1)^i Binomial[n, i], {i, 0, n}];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|