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A055327 Triangle of rooted identity trees with n nodes and k leaves. 7
1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 6, 5, 1, 9, 13, 2, 1, 12, 28, 11, 1, 16, 53, 40, 3, 1, 20, 91, 109, 26, 1, 25, 146, 254, 116, 6, 1, 30, 223, 524, 387, 61, 1, 36, 326, 998, 1068, 329, 12, 1, 42, 461, 1774, 2587, 1289, 145, 1, 49, 634, 2995, 5678, 4133, 911, 25, 1, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row lengths are 1,1,1,2,2,3,3,4,4,5,5,6,6,...

LINKS

Table of n, a(n) for n=1..67.

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

G.f. satisfies A(x,y) = x*y + x*WEIGH(A(x,y)) - x. Shifts up under WEIGH transform.

EXAMPLE

Triangle begins:

1;

1;

1;

1,  1;

1,  2;

1,  4,  1;

1,  6,  5;

1,  9, 13,  2;

1, 12, 28, 11;

1, 16, 53, 40, 3;

...

From Joerg Arndt, Aug 18 2014: (Start)

The identity trees with n=6 nodes, as (preorder-) level sequences, together with their number of leaves, and an ASCII rendering, are:

:

:     1:  [ 0 1 2 3 4 5 ]   1

:  O--o--o--o--o--o

:

:     2:  [ 0 1 2 3 4 3 ]   2

:  O--o--o--o--o

:        .--o

:

:     3:  [ 0 1 2 3 4 2 ]   2

:  O--o--o--o--o

:     .--o

:

:     4:  [ 0 1 2 3 4 1 ]   2

:  O--o--o--o--o

:  .--o

:

:     5:  [ 0 1 2 3 2 1 ]   3

:  O--o--o--o

:     .--o

:  .--o

:

:     6:  [ 0 1 2 3 1 2 ]   2

:  O--o--o--o

:  .--o--o

:

This gives [1, 4, 1], row n=6 of the triangle.

(End)

CROSSREFS

Row sums give A004111. Columns 2 through 8: A002620(n-2), A055328-A055333. Cf. A055334.

Sequence in context: A127625 A124844 A133934 * A105260 A099510 A211232

Adjacent sequences:  A055324 A055325 A055326 * A055328 A055329 A055330

KEYWORD

nonn,tabf,eigen

AUTHOR

Christian G. Bower, May 12 2000

STATUS

approved

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Last modified June 26 06:03 EDT 2017. Contains 288754 sequences.