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A052300 Number of rooted Greg trees. 8
1, 2, 6, 21, 78, 313, 1306, 5653, 25088, 113685, 523522, 2443590, 11533010, 54949539, 263933658, 1276652682, 6213207330, 30402727854, 149486487326, 738184395770, 3659440942282, 18205043615467, 90856842218506, 454770531433586, 2282393627458496, 11483114908752959 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A rooted Greg tree can be described as a rooted tree with 2-colored nodes where only the black nodes are counted and the white nodes have at least 2 children.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to rooted trees

N. J. A. Sloane, Transforms

FORMULA

Satisfies a = EULER(a) + SHIFT_RIGHT(EULER(a)) - a.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(a(i)+j-1, j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> `if`(n<1, 0, b(n-1$2)+b(n, n-1)):

seq(a(n), n=1..40);  # Alois P. Heinz, Jun 22 2018

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i] + j - 1, j] b[n - i j, i - 1], {j, 0, n/i}]]];

a[n_] := If[n < 1, 0, b[n - 1, n - 1] + b[n, n - 1]];

a /@ Range[1, 40] (* Jean-François Alcover, Oct 02 2019, after Alois P. Heinz *)

CROSSREFS

Cf. A005263, A005264, A048159, A048160, A052301-A052303.

Sequence in context: A150192 A287211 A150193 * A306832 A121941 A150194

Adjacent sequences:  A052297 A052298 A052299 * A052301 A052302 A052303

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Nov 15 1999

STATUS

approved

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Last modified December 6 07:08 EST 2019. Contains 329785 sequences. (Running on oeis4.)