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 A033536 Cubes of Catalan numbers (A000108). 9
 1, 1, 8, 125, 2744, 74088, 2299968, 78953589, 2924207000, 114933031928, 4738245926336, 203152294091656, 9000469593857728, 410006814589000000, 19129277941464384000, 911218671317138401125, 44202915427981062663000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of maximum independent vertex sets in the 3(n-1)-triangular honeycomb acute knight graph. - Eric W. Weisstein, Dec 31 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..500 Eric Weisstein's World of Mathematics, Catalan Number Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set FORMULA From Ilya Gutkovskiy, Jan 23 2017: (Start) O.g.f.: (1 - 3F2(-1/2,-1/2,-1/2; 1,1; 64*x))/(8*x). E.g.f.: 3F3(1/2,1/2,1/2; 2,2,2; 64*x). a(n) ~ 64^n/(Pi^(3/2)*n^(9/2)). (End) MAPLE seq((binomial(2*n, n)/(n+1))^3, n = 0..20); # G. C. Greubel, Oct 14 2019 MATHEMATICA Table[CatalanNumber@n^3, {n, 0, 20}] (* Vincenzo Librandi, Nov 13 2012 *) CatalanNumber[Range[0, 20]]^3 (* Eric W. Weisstein, Dec 31 2017 *) PROG (MuPAD) combinat::dyckWords::count(n)^3 \$ n = 0..16; // Zerinvary Lajos, Feb 15 2007 (Sage) [catalan_number(i)^3 for i in range(0, 17)] # Zerinvary Lajos, May 17 2009 (MAGMA) [Catalan(n)^3: n in [0..20]]; // Vincenzo Librandi, Nov 13 2012 (PARI) a(n) = (binomial(2*n, n)/(n+1))^3; \\ Altug Alkan, Dec 31 2017 (Sage) [catalan_number(n)^3 for n in (0..20)] # G. C. Greubel, Oct 14 2019 (GAP) List([0..20], n-> (Binomial(2*n, n)/(n+1))^3); # G. C. Greubel, Oct 14 2019 CROSSREFS Cf. A000108. Sequence in context: A264143 A110272 A215040 * A215793 A273279 A227851 Adjacent sequences:  A033533 A033534 A033535 * A033537 A033538 A033539 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 10 1999 STATUS approved

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Last modified January 18 00:43 EST 2022. Contains 350410 sequences. (Running on oeis4.)