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 A064345 Generalized Catalan numbers C(7,7; n). 1
 1, 1, 14, 833, 83006, 10213854, 1404124008, 206635997673, 31844571309110, 5073749573133710, 829012595472718580, 138151786440502006186, 23390450962161609522028, 4012173837912126230070832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references. LINKS J. Abate, W. Whitt, Brownian Motion and the Generalized Catalan Numbers, J. Int. Seq. 14 (2011) # 11.2.6, corollary 6. FORMULA a(n)= ((7^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/7)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1). G.f.:(1-13*x*c(49*x))/(1-7*x*c(49*x))^2 = c(49*x)*(13+36*c(49*x))/(1+6*c(49*x))^2 = (13*c(49*x)*(7*x)^2+12*(3+10*x))/(6+7*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108. 6*(-n+1)*a(n) +7*(167*n-420)*a(n-1) +686*(2*n-3)*a(n-2)=0. - R. J. Mathar, Aug 09 2017 CROSSREFS Sequence in context: A050983 A183576 A002429 * A269335 A159871 A340259 Adjacent sequences: A064342 A064343 A064344 * A064346 A064347 A064348 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Oct 12 2001 STATUS approved

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)