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A064089 Generalized Catalan numbers C(6; n). 3
1, 1, 7, 85, 1279, 21517, 387607, 7312789, 142648495, 2853691357, 58226571271, 1207062556261, 25351452769567, 538285926177325, 11535690316148215, 249189167966657845, 5420206822556721295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1)= Y_{n}(n+1)= Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=6, beta =1 (or alpha=1, beta=6).

LINKS

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

FORMULA

G.f.: (1+6*x*c(6*x)/5)/(1+x/5) = 1/(1-x*c(6*x)) with c(x) g.f. of Catalan numbers A000108.

a(n)= sum((n-m)*binomial(n-1+m, m)*(6^m)/n, m=0..n-1) = ((-1/5)^n)*(1-6*sum(C(k)*(-30)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).

a(n) = Sum{ k= 0...n, A059365(n, k)*6^(n-k) } . - Philippe Deléham, Jan 19 2004

Conjecture: 5*n*a(n) +(-119*n+180)*a(n-1) +12*(-2*n+3)*a(n-2)=0. - R. J. Mathar, Jun 07 2013

PROG

(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-5*x^2)/(1+x)^2+O(x^(n+1))), n)) /* Ralf Stephan */

CROSSREFS

A064088 (C(5, n)).

Sequence in context: A126344 A193578 A026001 * A216698 A317353 A302565

Adjacent sequences:  A064086 A064087 A064088 * A064090 A064091 A064092

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 13 2001

STATUS

approved

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Last modified October 23 16:15 EDT 2018. Contains 316529 sequences. (Running on oeis4.)