|
|
A285855
|
|
Number of permutations of [n] with four ordered cycles such that equal-sized cycles are ordered with increasing least elements.
|
|
3
|
|
|
1, 40, 430, 6300, 62601, 706608, 8985560, 107911760, 1439518696, 20364348576, 304923257184, 4772610024000, 80570363703696, 1409795519233536, 26263500315144192, 511153327733815296, 10464902116976779776, 223154458395064842240, 5010190272214829475840
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
4,2
|
|
LINKS
|
|
|
MAPLE
|
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 5)
end:
a:= n-> coeff(b(n$2, 0), x, 4):
seq(a(n), n=4..25);
|
|
MATHEMATICA
|
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 4}];
a[n_] := Coefficient[b[n, n, 0], x, 4];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|