|
|
A004114
|
|
Number of trees with n nodes and 2-colored internal (non-leaf) nodes.
(Formerly M1422)
|
|
18
|
|
|
1, 1, 1, 2, 5, 12, 33, 98, 305, 1002, 3424, 12016, 43230, 158516, 590621, 2230450, 8521967, 32889238, 128064009, 502590642, 1986357307, 7900377892, 31602819524, 127076645038, 513419837168, 2083414420394, 8488377206876, 34712566540014, 142443837953632
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c * d^n / n^(5/2), where d = 4.49415643203339504537343052... (same as for A004113), c = 0.31497820931312537077... . - Vaclav Kotesovec, Sep 12 2014
|
|
MATHEMATICA
|
max = 28; etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n ]; b]; bb = etr[A004113]; A004113[n_] := If[n <= 1, n, 2*bb[n - 1]]; b[x_] := Sum[A004113[n] x^n, {n, 1, max}]; f[x_] := Sum[a[n] x^n, {n, 0, max}]; a[0] = a[1] = a[2] = 1; coes = CoefficientList[ Series[f[x] - (1 + b[x] - x*b[x] - b[x]^2/2 + b[x^2]/2), {x, 0, max}], x]; Table[a[n], {n, 0, max}] /. Solve[Thread[coes == 0]][[1]] (* Jean-François Alcover, Jan 29 2013, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|