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A064329 Generalized Catalan numbers C(-7; n). 3
1, 1, -6, 85, -1490, 29226, -614004, 13511709, -307448490, 7174776190, -170777485556, 4130050311234, -101192982385844, 2506610481299380, -62668163792277840, 1579300030107459885, -40076101342241993370 (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

Table of n, a(n) for n=0..16.

FORMULA

a(n)= sum((n-m)*binomial(n-1+m, m)*((-7)^m)/n, m=0..n-1) = ((1/8)^n)*(1+7*sum(C(k)*(-7*8)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).

G.f.: (1+7*x*c(-7*x)/8)/(1-x/8) = 1/(1-x*c(-7*x)) with c(x) g.f. of Catalan numbers A000108.

CROSSREFS

Sequence in context: A290011 A164266 A136597 * A187740 A209035 A230782

Adjacent sequences:  A064326 A064327 A064328 * A064330 A064331 A064332

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Sep 21 2001

STATUS

approved

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Last modified October 23 07:20 EDT 2018. Contains 316520 sequences. (Running on oeis4.)