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A064333 Generalized Catalan numbers C(-11; n). 2
1, 1, -10, 221, -6082, 187386, -6184848, 213843477, -7645509706, 280351640702, -10485617230780, 398467433529298, -15341431926699284, 597149747213056324, -23459916801814723548, 929028306450848244741, -37045540042729366580442 (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)*((-11)^m)/n, m=0..n-1) = ((1/12)^n)*(1+11*sum(C(k)*(-11*12)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).

G.f.: (1+11*x*c(-11*x)/12)/(1-x/12) = 1/(1-x*c(-11*x)) with c(x) g.f. of Catalan numbers A000108.

CROSSREFS

Sequence in context: A166181 A199748 A210137 * A223817 A229256 A052789

Adjacent sequences:  A064330 A064331 A064332 * A064334 A064335 A064336

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Sep 21 2001

STATUS

approved

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Last modified February 23 15:43 EST 2018. Contains 299581 sequences. (Running on oeis4.)