This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A064326 Generalized Catalan numbers C(-4; n). 2
 1, 1, -3, 25, -251, 2817, -33843, 425769, -5537835, 73865617, -1004862179, 13888533561, -194475377243, 2752994728225, -39333541106835, 566464908534345, -8214515461250955, 119845125957958065, -1757855400878129475, 25906894146115000665, -383443906519878272955 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See triangle A064334 with columns m built from C(-m; n), m >= 0, also for Derrida et al. references. LINKS FORMULA a(n) = sum((n-m)*binomial(n-1+m, m)*((-4)^m)/n, m=0..n-1) = ((1/5)^n)*(1+4*sum(C(k)*(-4*5)^k, k=0..n-1)), n >= 1, a(0) = 1; with C(n) = A000108(n) (Catalan). G.f.: (1+4*x*c(-4*x)/5)/(1-x/5) = 1/(1-x*c(-4*x)) with c(x) g.f. of Catalan numbers A000108. a(n) = hypergeometric([1-n, n], [-n], -4) for n>0. - Peter Luschny, Nov 30 2014 PROG (Sage) def a(n):     if n==0: return 1     return hypergeometric([1-n, n], [-n], -4).simplify() [a(n) for n in range(20)] # Peter Luschny, Nov 30 2014 CROSSREFS Cf. A064334. Sequence in context: A245925 A260209 A086655 * A006091 A009042 A080896 Adjacent sequences:  A064323 A064324 A064325 * A064327 A064328 A064329 KEYWORD sign,easy AUTHOR Wolfdieter Lang, Sep 21 2001 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)