%I A089408
%S A089408 1,1,2,1,2,2,4,5,10,14,28,42,84,132,264,429,858,1430,2860,4862,9724,
%T A089408 16796,33592,58786,117572,208012,416024,742900,1485800,2674440,5348880,
%U A089408 9694845,19389690,35357670,70715340,129644790,259289580,477638700
%N A089408 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation 
               A089864.
%C A089408 The number of n-node binary trees fixed by the corresponding automorphism(s). 
               Essentially A000108 interleaved with A068875.
%H A089408 A. Karttunen, <a href="a089408.c.txt">C-program for computing the initial 
               terms of this sequence</a>
%F A089408 a(0)=1, a(2n) = 2*A000108(n-1), a(2n+1) = A000108(n)
%F A089408 G.f.: (1+4x-(1+2x)sqrt(1-4x^2))/(2x) - Paul Barry (pbarry(AT)wit.ie), 
               Apr 11 2005
%F A089408 C(2*j,j)/(1+j)*i, i=1..2),j>=0. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 29 2007
%p A089408 seq(seq(binomial(2*j,j)/(1+j)*i, i=1..2),j=0..19); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 29 2007
%o A089408 (Scheme) (define (A089408 n) (cond ((zero? n) 1) ((even? n) (* 2 (A000108 
               (-1+ (/ n 2))))) (else (A000108 (/ (-1+ n) 2)))))
%Y A089408 Cf. A089402.
%Y A089408 Cf. A000108.
%Y A089408 Sequence in context: A163373 A117193 A026832 this_sequence A079318 A050315 
               A128978
%Y A089408 Adjacent sequences: A089405 A089406 A089407 this_sequence A089409 A089410 
               A089411
%K A089408 nonn,easy
%O A089408 0,3
%A A089408 Antti Karttunen (His_Firstname.His_Surname(AT)gmail.com), Nov 29 2003