|
|
A309996
|
|
Number of forests of rooted identity trees with 2n colored nodes using exactly n colors.
|
|
2
|
|
|
1, 1, 60, 10746, 4191916, 2894100710, 3128432924009, 4887094401176148, 10429904418286375276, 29174096160751011237987, 103602945849963939278211780, 455474137757927866858846385930, 2428879210633773939611859814825540, 15447942216555014401018067561180236424
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(n, k) option remember; `if`(n<2, n, add(b(n-j, k)*add(b(d, k)
*k*d*(-1)^(j/d+1), d=numtheory[divisors](j)), j=1..n-1)/(n-1))
end:
a:= n-> add(b(2*n+1, 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 < 2, n, Sum[b[n - j, k]*Sum[b[d, k]*k*d*(-1)^(j/d+1), {d, Divisors[j]}], {j, 1, n-1}]/(n-1)];
a[n_] := Sum[b[2*n+1, n-i]*(-1)^i*Binomial[n, i], {i, 0, n}];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|