|
Search: id:A064091
|
|
|
| A064091 |
|
Generalized Catalan numbers C(8; n). |
|
+0
3
|
|
| 1, 1, 9, 145, 2905, 65121, 1563561, 39322929, 1022586105, 27272680705, 741894295369, 20504949587409, 574176887116441, 16254518495907745, 464436319229036265, 13376293681432402545, 387925710986712480825
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
a(n+1)= Y_{n}(n+1)= Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=8, beta =1 (or alpha=1, beta=8).
|
|
FORMULA
|
G.f.: (1+8*x*c(8*x)/7)/(1+x/7) = 1/(1-x*c(8*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)=sum((n-m)*binomial(n-1+m, m)*(8^m)/n, m=0..n-1) = ((-1/7)^n)*(1-8*sum(C(k)*(-56)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
a(n) = Sum{ k= 0...n, A059365(n, k)*8^(n-k) } . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-7*x^2)/(1+x)^2+O(x^(n+1))), n)) (from R. Stephan)
|
|
CROSSREFS
|
A064090 (C(7, n)).
Sequence in context: A034829 A094594 A046529 this_sequence A132060 A006691 A050580
Adjacent sequences: A064088 A064089 A064090 this_sequence A064092 A064093 A064094
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2001
|
|
|
Search completed in 0.002 seconds
|
