A072638 Number of unary-binary rooted trees of height at most n.
0, 1, 3, 10, 66, 2278, 2598060, 3374961778891, 5695183504492614029263278, 16217557574922386301420536972254869595782763547560
Offset: 0
Keywords
Crossrefs
Programs
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Maple
a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n-1]+2,2) od: seq(a[n], n=-1..9); # Zerinvary Lajos, Jun 08 2007
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Mathematica
Clear[a]; a[0] = 0; a[n_] := a[n] = 1 + (a[n-1]*(a[n-1]+3))/2; Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Jan 31 2013 *)
Formula
a(n+1) = 1 + (a(n)*(a(n)+3))/2.
Conjecture: a(n) = A006894(n+1) - 1. - R. J. Mathar, Apr 23 2007
a(n) := C(a(n-1) + 2, 2), n >= -1. - Zerinvary Lajos, Jun 08 2007
Extensions
Edited by Christian G. Bower, Oct 23 2002
Comments