|
Search: id:A064327
|
|
|
| A064327 |
|
Generalized Catalan numbers C(-5; n). |
|
+0
4
|
|
| 1, 1, -4, 41, -514, 7206, -108174, 1700721, -27646234, 460887086, -7836596944, 135380098426, -2369445113804, 41925242220616, -748729419265314, 13478117036893281, -244306305241572474, 4455242518055441046
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
See triangle A064334 with columns m built from C(-m; n), m >= 0, also for Derrida et al. references.
|
|
FORMULA
|
a(n)= sum((n-m)*binomial(n-1+m, m)*((-5)^m)/n, m=0..n-1) = ((1/6)^n)*(1+5*sum(C(k)*(-5*6)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+5*x*c(-5*x)/6)/(1-x/6) = 1/(1-x*c(-5*x)) with c(x) g.f. of Catalan numbers A000108.
|
|
CROSSREFS
|
Sequence in context: A118450 A024383 A110041 this_sequence A134277 A085340 A001908
Adjacent sequences: A064324 A064325 A064326 this_sequence A064328 A064329 A064330
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 21 2001
|
|
|
Search completed in 0.002 seconds
|
