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A024358
Sum of the sizes of binary subtrees of the perfect binary tree of height n.
3
0, 1, 8, 105, 6136, 8766473, 8245941529080, 3508518207951157937469961, 311594265746788494170062926869662848646207622648, 1217308491239906829392988008143949647398943617188660186130545502913055217344025410733271773705
OFFSET
0,3
COMMENTS
Size of binary tree = number of internal nodes.
FORMULA
a(n) = B'_n(1) where B_{n+1}(x) = 1 + x*B_n(x)^2.
From Alois P. Heinz, Jul 12 2019: (Start)
a(n) = Sum_{k=0..2^n-1} (2^n-1-k) * A309049(2^n-1,k).
a(n) = A309052(2^n-1). (End)
MAPLE
B:= proc(n) B(n):= `if`(n<0, 0, expand(1+x*B(n-1)^2)) end:
a:= n-> subs(x=1, diff(B(n), x)):
seq(a(n), n=0..9); # Alois P. Heinz, Jul 12 2019
MATHEMATICA
B[n_] := If[n<0, 0, Expand[1+x*B[n-1]^2]];
a[n_] := D[B[n], x] /. x -> 1;
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Oct 13 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cyril Banderier, Jun 09 2000
EXTENSIONS
a(0) changed to 0 by Alois P. Heinz, Jul 12 2019
STATUS
approved