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A036602 Triangle of coefficients of generating function of binary rooted trees of height at most n. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 3, 5, 6, 8, 8, 9, 7, 7, 4, 3, 1, 1, 1, 1, 1, 2, 3, 6, 10, 17, 25, 38, 52, 73, 93, 121, 143, 172, 187, 205, 202, 201, 177, 158, 123, 99, 66, 47, 26, 17, 7, 4, 1, 1, 1, 1, 1, 2, 3, 6, 11, 22, 39, 70, 118, 200, 324, 526 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Alois P. Heinz, Rows n = 0..12, flattened

E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees), J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.

Index entries for sequences related to rooted trees

EXAMPLE

Triangle begins:

1

1, 1;

1, 1, 1, 1;

1, 1, 1, 2, 2, 2,  1,  1;

1, 1, 1, 2, 3, 5,  6,  8,  8,  9,   7,   7,   4,    3,    1,    1;

1, 1, 1, 2, 3, 6, 10, 17, 25, 38,  52,  73,  93,  121,  143,  172,  187, ...

1, 1, 1, 2, 3, 6, 11, 22, 39, 70, 118, 200, 324,  526,  825, 1290, 1958, ...

1, 1, 1, 2, 3, 6, 11, 23, 45, 90, 171, 325, 598, 1097, 1972, 3531, 6225, ...

MAPLE

b:= proc(n, h) option remember; `if`(n<2, n, `if`(h<1, 0, `if`(n::odd, 0,

     (t-> t*(1-t)/2)(b(n/2, h-1)))+add(b(i, h-1)*b(n-i, h-1), i=1..n/2)))

    end:

A:= (n, k)-> b(k+1, n):

seq(seq(A(n, k), k=0..2^n-1), n=0..6);  # Alois P. Heinz, Sep 08 2017

MATHEMATICA

b[n_, h_] := b[n, h] = If[n < 2, n, If[h < 1, 0, If[OddQ[n], 0, Function[t, t*(1-t)/2][b[n/2, h-1]]] + Sum[b[i, h-1]*b[n-i, h-1], {i, 1, n/2}]]];

A[n_, k_] := b[k+1, n];

Table[Table[A[n, k], {k, 0, 2^n-1}], {n, 0, 6}] // Flatten (* Jean-Fran├žois Alcover, Feb 14 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A001190, A036587, A036588, A036589, A036590, A036591, A036592.

Sequence in context: A327104 A126061 A088496 * A176166 A167911 A037804

Adjacent sequences:  A036599 A036600 A036601 * A036603 A036604 A036605

KEYWORD

nonn,tabf,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 6 10:00 EST 2021. Contains 341846 sequences. (Running on oeis4.)