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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064345 Generalized Catalan numbers C(7,7; n). 1

%I

%S 1,1,14,833,83006,10213854,1404124008,206635997673,31844571309110,

%T 5073749573133710,829012595472718580,138151786440502006186,

%U 23390450962161609522028,4012173837912126230070832

%N Generalized Catalan numbers C(7,7; n).

%C See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references.

%H J. Abate, W. Whitt, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Whitt/whitt6.html">Brownian Motion and the Generalized Catalan Numbers</a>, J. Int. Seq. 14 (2011) # 11.2.6, corollary 6.

%F a(n)= ((7^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/7)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).

%F G.f.:(1-13*x*c(49*x))/(1-7*x*c(49*x))^2 = c(49*x)*(13+36*c(49*x))/(1+6*c(49*x))^2 = (13*c(49*x)*(7*x)^2+12*(3+10*x))/(6+7*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.

%F 6*(-n+1)*a(n) +7*(167*n-420)*a(n-1) +686*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017

%Y A064344.

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 12 2001

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 July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)