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%I #16 Mar 24 2021 11:47:05
%S 3,24,675,458328,210066388899,44127887745906175987800,
%T 1947270476915296449559703445493848930452791203,
%U 3791862310265926082868235028027893277370233152247388584761734150717768254410341175325352024
%N Number of binary trees of height <= n.
%D Todd K. Moon, "Enumerations of binary trees, types of trees and the number of reversible variable length codes," submitted to Discrete Applied Mathematics, 2000.
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F a(n) = d(n) + a(n-1), d(n) = A001699(n) is the number of binary trees of depth exactly n.
%F a(n) = A003095(n+2) - 2 = A004019(n+1) - 1 = a(n-1)^2 + 4*a(n-1) + 3.
%o (Python)
%o from itertools import accumulate
%o def f(anm1, _): return anm1**2 + 4*anm1 + 3
%o def aupton(terms): return list(accumulate([3]*terms, f))
%o print(aupton(8)) # _Michael S. Branicky_, Mar 24 2021
%Y Cf. A001699, A002449, A003095.
%K easy,nonn
%O 1,1
%A Todd K. Moon (Todd.Moon(AT)ece.usu.edu), Aug 02 2000
%E More terms from _Henry Bottomley_, Jul 09 2001
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