login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160823 A transform of the large Schroeder numbers. 2
1, 1, 3, 5, 13, 27, 69, 161, 415, 1033, 2701, 6983, 18521, 49041, 131723, 354493, 962381, 2620675, 7178285, 19724513, 54430023, 150641937, 418294813, 1164528399, 3250685297, 9094701729, 25501672595, 71649158709, 201687341901 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A060656(n+1).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-x^2/(1-...))))))) (continued fraction);

G.f.: (1-x-x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(2*x^2*(1-x)).

a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*A006318(k).

Conjecture: (n+2)*a(n) -3*(n+1)*a(n-1) +3(2-n)*a(n-2) +(11*n-20)*a(n-3) +(11-5*n)*a(n-4) + (4-n)*a(n-5)=0. - R. J. Mathar, Nov 16 2011

a(n) ~ sqrt((-36 + 63*sqrt(2) + sqrt(8666 - 4936*sqrt(2)))/8) * ((1 + sqrt(13 + 8*sqrt(2)))/2)^n / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, May 01 2018

EXAMPLE

G.f. = 1 + x + 3*x^2 + 5*x^3 + 13*x^4 + 27*x^5 + 69*x^6 + 161*x^7 + ...

MATHEMATICA

CoefficientList[Series[(1-x-x^2-Sqrt[1-2*x-5*x^2+6*x^3+x^4])/(2*x^2*(1- x)), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2018 *)

PROG

(PARI) x='x+O('x^50); Vec((1-x-x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(2*x^2*(1-x))) \\ G. C. Greubel, Apr 30 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-x^2-Sqrt(1-2*x-5*x^2+6*x^3+x^4))/(2*x^2*(1-x)))); // G. C. Greubel, Apr 30 2018

CROSSREFS

Sequence in context: A026569 A035082 A005198 * A077443 A147196 A110225

Adjacent sequences:  A160820 A160821 A160822 * A160824 A160825 A160826

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 27 2009

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 January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)