|
Search: id:A064310
|
|
|
| A064310 |
|
Generalized Catalan numbers C(-1; n). |
|
+0
9
|
|
| 1, 1, 0, 1, -2, 6, -18, 57, -186, 622, -2120, 7338, -25724, 91144, -325878, 1174281, -4260282, 15548694, -57048048, 210295326, -778483932, 2892818244, -10786724388, 40347919626, -151355847012, 569274150156
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
See triangle A064334 with columns m built from C(-m; n), m >= 0, also for Derrida et al. references.
Unsigned sequence with a(0) := 0 is A000957 (Fine).
|
|
FORMULA
|
a(n)= sum((n-m)*binomial(n-1+m, m)*((-1)^m)/n, m=0..n-1) = ((1/2)^n)*(1+sum(C(k)*(-2)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+x*c(-x)/2)/(1-x/2) = 1/(1-x*c(-x)) with c(x) g.f. of Catalan numbers A000108.
a(n) = Sum_{k, 0<=k<=n} (-1)^(n-k)*A106566(n, k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 18 2005
(-1)^n*a(n)=Sum_{k, 0<=k<=n}A039599(n,k)*(-2)^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 13 2007
|
|
CROSSREFS
|
Sequence in context: A111961 A071721 A125306 this_sequence A126983 A104629 A000957
Adjacent sequences: A064307 A064308 A064309 this_sequence A064311 A064312 A064313
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 21 2001
|
|
|
Search completed in 0.002 seconds
|
