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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
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.
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-François Alcover, Feb 14 2021, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A327104 A126061 A088496 * A176166 A167911 A037804
KEYWORD
nonn,tabf,nice,easy
AUTHOR
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)