A038058 Number of labeled trees with 2-colored nodes.

1, 2, 4, 24, 256, 4000, 82944, 2151296, 67108864, 2448880128, 102400000000, 4829076871168, 253613523861504, 14681377947951104, 928873060356849664, 63772920000000000000, 4722366482869645213696, 375183514207494575620096

Offset: 0

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..321
• Index entries for sequences related to trees

Crossrefs

Cf. A000272, A038055-A038062.

Programs

Maple

1, seq(2^n * n^(n-2), n=1..20); # Robert Israel, Nov 02 2014

Mathematica

nn = 17; f[x_] := Sum[n^(n - 2) x^n/n!, {n, 1, nn}];
Range[0, nn]! CoefficientList[Series[f[2 x] + 1, {x, 0, nn}], x] (* Geoffrey Critzer, Nov 02 2014 *)

Formula

a(n) = A038057(n)/n = 2^n * n^(n-2) for n>=1. E.g.f. B(2*x) where B(x) is e.g.f. of A000272.