Search: id:A005755
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%I A005755 M3517
%S A005755 0,0,0,1,4,16,64,252,1018,4182,17510,74510,322034,1410362,6251114,
%T A005755 27998532,126583634,577079333,2650573354,12256481666,57021299394,
%U A005755 266754944481,1254245360430,5924659521632,28105641930102
%N A005755 Number of identity matched trees with n nodes.
%D A005755 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005755 R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 
               (1991), 93-104.
%H A005755 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%p A005755 with(numtheory): b2:= proc(n) option remember; local m; `if` (n=1, 1, 
               2/(n-1) *add (b2(m) *add((-1)^((n-m)/d+1) *d*b2(d), d=divisors(n-m)), 
               m=1..n-1)) end: c2:= proc(n) option remember; local m; `if` (n=1, 
               1, 1/(n-1) *add (c2(m) *add((-1)^((n-m)/d+1) *d*b2(d), d=divisors(n-m)), 
               m=1..n-1)) end: a2:= n-> (b2(n) -add (b2(m) *b2(n-m), m=1..n-1) -`if` 
               (irem(n, 2)=0, b2(n/2), c2((n+1)/2)))/2: seq (a2(n), n=1..30); [From 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009]
%Y A005755 Sequence in context: A027676 A065738 A006811 this_sequence A077821 A000302 
               A050734
%Y A005755 Adjacent sequences: A005752 A005753 A005754 this_sequence A005756 A005757 
               A005758
%K A005755 nonn
%O A005755 1,5
%A A005755 N. J. A. Sloane (njas(AT)research.att.com).
%E A005755 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009

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