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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A098618 Products of A007482 and Catalan numbers: a(n) = A007482(n)*A000108(n). 3
1, 3, 22, 195, 1946, 20790, 232716, 2693691, 31979090, 387243714, 4764470932, 59391201870, 748472730628, 9520446996300, 122067269204760, 1575965219205195, 20470515781159170, 267325017886787850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Radius of convergence: r = (sqrt(17)-3)/16; A(r) = sqrt(2+6/sqrt(17)). Recurrence of A007482 is A007482(n) = 3*A007482(n-1) + 2*A007482(n-2). More generally, given {S} such that: S(n) = b*S(n-1) + c*S(n-2), |b|>0, |c|>0, then Sum_{n>=0} S(n)*Catalan(n)*x^n = sqrt( (1-2*b*x - sqrt(1-4*b*x-16*c*x^2))/(2*b^2+8*c) )/x.

LINKS

Table of n, a(n) for n=0..17.

FORMULA

G.f.: A(x) = sqrt((1-6*x - sqrt(1-12*x-32*x^2))/34 )/x.

n*(n+1)*a(n) -6*n*(2*n-1)*a(n-1) -8*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 17 2018

EXAMPLE

Begins: {1*1, 3*1, 11*2, 39*5, 139*14, 495*42, 1763*132, 6279*429,...}.

PROG

(PARI) {a(n)=binomial(2*n, n)/(n+1)*((3+sqrt(17))^(n+1)-(3-sqrt(17))^(n+1))/2^(n+1)/sqrt(17)}

CROSSREFS

Cf. A007482, A000108, A098614, A098616, A098619.

Sequence in context: A046743 A121952 A250888 * A207326 A006783 A330668

Adjacent sequences:  A098615 A098616 A098617 * A098619 A098620 A098621

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 09 2004

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 December 4 02:18 EST 2020. Contains 338921 sequences. (Running on oeis4.)