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A006930 Binomial transform of rooted tree numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)