Search: id:A051179
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%I A051179
%S A051179 1,3,15,255,65535,4294967295,18446744073709551615,340282366920938463463374607431768211455,
%T A051179 115792089237316195423570985008687907853269984665640564039457584007913129639935
%N A051179 2^(2^n)-1.
%C A051179 In a tree with binary nodes (0, 1 children only), the maximum number 
               of unique child nodes at level n.
%C A051179 Number of binary trees (each vertex has 0, or 1 left, or 1 right, or 
               2 children) such that all leaves are at level n. Example: a(1) = 
               3 because we have (i) root with a left child, (ii) root with a right 
               child and (iii) root with two children. a(n)=A000215(n)-2. - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Jan 20 2004
%C A051179 The first 5 terms n (only) have the prpoerty that phi(n)=(n+1)/2, where 
               phi(n)=A000010(n) is Euler's totient function. - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), Feb 12 2007
%D A051179 M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, Berlin, 
               1999; see p. 4.
%H A051179 For rate of growth see A. V. Aho and N. J. A. Sloane, <a href="http:/
               /www.research.att.com/~njas/doc/doubly.html">Some doubly exponential 
               sequences</a>, Fib. Quart., 11 (1973), 429-437.
%H A051179 <a href="Sindx_Aa.html#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 
               + ...</a>
%F A051179 a(n) = (a(n-1) + 1)^2 - 1, a(0) = 1. [ or a(n) = a(n-1)(a(n-1) + 2) ].
%F A051179 1 = 2/3 + 4/15 + 16/255 + 256/65535...= Sum(0 through infinity) A001146(n)/
               a(n+1); with partial sums: 2/3, 14/15, 254/255, 65534/65535... - 
               Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2003
%F A051179 a(n)=b(n-1) where b(1)=1, b(n) = prod(k=1, n-1, b(k)+2) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Sep 13 2003
%o A051179 (PARI) a(n)=if(n<0,0,2^2^n-1)
%Y A051179 Cf. A001146, A007018. Partial products of A000215.
%Y A051179 a(n)=A000215(n)-2.
%Y A051179 Sequence in context: A139289 A116518 A050474 this_sequence A122591 A120607 
               A013352
%Y A051179 Adjacent sequences: A051176 A051177 A051178 this_sequence A051180 A051181 
               A051182
%K A051179 nonn,easy,nice
%O A051179 0,2
%A A051179 Alan DeKok (aland(AT)ox.org)

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