A006930 Binomial transform of rooted tree numbers.

1, 2, 5, 14, 42, 131, 420, 1376, 4589, 15537, 53293, 184881, 647752, 2289215, 8152147, 29226618, 105408688, 382193502, 1392377762, 5094356032, 18711122069, 68965586862, 255006331944, 945662753514, 3516281928159, 13106923073426, 48967229534156, 183326438562982

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..600

Index entries for sequences related to rooted trees

N. J. A. Sloane, Transforms

Formula

a(n) ~ c * d^n / n^(3/2), where d = 1 + A051491 = 3.955765285651994974714..., c = 2.0132071688691451819... . - Vaclav Kotesovec, Aug 25 2014

Maple

with(numtheory):
b:= proc(n) option remember; local d, j; `if`(n<=1, n,
      (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
    end:
a:= n-> add(b(k+1)*binomial(n, k), k=0..n):
seq(a(n), n=0..30);  # Alois P. Heinz, May 17 2013

Mathematica

b[n_] := b[n] = Module[{d, j}, If[n <= 1, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]]; a[n_] := Sum[b[k+1]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 07 2014, translated from Maple *)

Crossrefs

Cf. A000081, A051491.

Sequence in context: A196417 A054392 A261588 * A036767 A261894 A287969

Adjacent sequences: A006927 A006928 A006929 * A006931 A006932 A006933

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved