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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 November 27 09:38 EST 2020. Contains 338679 sequences. (Running on oeis4.)