A309996 Number of forests of rooted identity trees with 2n colored nodes using exactly n colors.

1, 1, 60, 10746, 4191916, 2894100710, 3128432924009, 4887094401176148, 10429904418286375276, 29174096160751011237987, 103602945849963939278211780, 455474137757927866858846385930, 2428879210633773939611859814825540, 15447942216555014401018067561180236424

Offset: 0

Author

Alois P. Heinz, Aug 26 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..188

Crossrefs

Cf. A256068.

Programs

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}];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Sep 15 2022, after Alois P. Heinz *)

Formula

a(n) = A256068(2n+1,n).