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A064330 Generalized Catalan numbers C(-8; n). 2
1, 1, -7, 113, -2263, 50721, -1217703, 30622929, -796311415, 21237226625, -577699502407, 15966537989425, -447086291268119, 12656524451911393, -361628025405250023, 10415207118205622673, -302049007052246016183 (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)*((-8)^m)/n, m=0..n-1) = ((1/9)^n)*(1+8*sum(C(k)*(-8*9)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).

G.f.: (1+8*x*c(-8*x)/9)/(1-x/9) = 1/(1-x*c(-8*x)) with c(x) g.f. of Catalan numbers A000108.

CROSSREFS

Sequence in context: A084974 A156240 A152927 * A159552 A228929 A086788

Adjacent sequences:  A064327 A064328 A064329 * A064331 A064332 A064333

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Sep 21 2001

STATUS

approved

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Last modified February 20 03:12 EST 2018. Contains 299357 sequences. (Running on oeis4.)