login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089849 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A069772. 2
1, 1, 2, 1, 6, 2, 20, 5, 70, 14, 252, 42, 924, 132, 3432, 429, 12870, 1430, 48620, 4862, 184756, 16796, 705432, 58786, 2704156, 208012, 10400600, 742900, 40116600, 2674440, 155117520, 9694845, 601080390, 35357670, 2333606220, 129644790 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of n-node binary trees fixed by the corresponding automorphism(s). A000984 interleaved with A000108.

LINKS

Table of n, a(n) for n=0..35.

A. Karttunen, C-program for computing the initial terms of this sequence

FORMULA

a(2n) = A000984(n), a(2n+1) = A000108(n)

a(n)=sum{k=0..floor(n/2), C(k)C(k+1, n-k)} - Paul Barry, Feb 23 2005

a(n+1)=Jacobi_P(n, 2, 0, 0)*2^n*(cos(pi*n/2)+sin(pi*n/2)); a(n+1)=sum{k=0..n, C(n, k)C(n+2, k)(-1)^k}*(cos(pi*n/2)+sin(pi*n/2)); - Paul Barry, Jan 23 2006

From Sergei N. Gladkovskii, Dec 18 2012 (Start)

E.g.f.: 1+int(G(0))dx where G(k) =  1 + 2*x/(1 - 2*x/(2*x + (2*k+2)*(2*k+4)/G(k+1) )); (recursively defined continued fraction).

E.g.f.: 1+x*G(0) where G(k) = 1 + x*(2*k+1)/(k+1 - x*(k+1)/(x + (k+2)*(2*k+3)/G(k+1) )); (recursively defined continued fraction).

E.g.f.:E(x) = int( (1/x + 2)*BesselI(1,2*x) )dx . (End)

G.f.: G(0), where G(k)= 1 + x/(k+1 - (k+1)*(4*k+2)*x/((4*k+2)*x + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 19 2013

PROG

(Scheme) (define (A089849 n) (if (even? n) (A000984 (/ n 2)) (A000108 (/ (- n 1) 2))))

CROSSREFS

Cf. A089880.

Sequence in context: A057560 A085592 A174421 * A185330 A217955 A325703

Adjacent sequences:  A089846 A089847 A089848 * A089850 A089851 A089852

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Nov 29 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 7 19:13 EST 2021. Contains 341928 sequences. (Running on oeis4.)