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 A068765 Generalized Catalan numbers. 1
 1, 1, 6, 39, 270, 1962, 14796, 114831, 911574, 7368894, 60457428, 502162902, 4214515212, 35686162548, 304491863448, 2615468845311, 22598114065254, 196269877811574, 1712578870493316, 15005719955119698 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)=K(3,3; n)/3 with K(a,b; n) defined in a comment to A068763. LINKS Fung Lam, Table of n, a(n) for n = 0..1000 FORMULA a(n)=(3^n)*p(n, -2/3) with the row polynomials p(n, x) defined from array A068763. a(n+1)= 3*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1). G.f.: (1-sqrt(1-12*x*(1-2*x)))/(6*x). Recurrence: (n+1)*a(n) = 24*(2-n)*a(n-2) + 6*(2*n-1)*a(n-1). - Fung Lam, Mar 04 2014 a(n) ~ sqrt(6+6*sqrt(3)) * (6+2*sqrt(3))^n / (6*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 04 2014 MATHEMATICA CoefficientList[Series[(1-Sqrt[1-12*x*(1-2*x)])/(6*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 04 2014 *) CROSSREFS Cf. A000108, A068764, A068766-72, A025227-30. Sequence in context: A199491 A147961 A264232 * A006633 A153392 A253077 Adjacent sequences:  A068762 A068763 A068764 * A068766 A068767 A068768 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Mar 04 2002 STATUS approved

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Last modified January 16 10:52 EST 2021. Contains 340206 sequences. (Running on oeis4.)