A133054 Cubes of Motzkin numbers.

1, 1, 8, 64, 729, 9261, 132651, 2048383, 33698267, 582182875, 10474708672, 194910229592, 3731808877831, 73218245857875, 1467320155924104, 29956212068269248, 621670415400598563, 13090510375656917139, 279262277830549534968, 6027856524470650538304

Offset: 0

Author

Omar E. Pol, Oct 30 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..700

Crossrefs

Cf. A000578, A030078, A056570.

Motzkin numbers: A001006.

Programs

Maple

a1006:= gfun:-rectoproc({(-3*x-6)*a(x+1)+(-2*x-7)*a(x+2)+(x+5)*a(x+3), a(0) = 1, a(1) = 1, a(2) = 2},a(x),remember):
map(a1006^3, [$0..60]); # Robert Israel, Oct 03 2017

Mathematica

CoefficientList[Series[(1 - x - (1 - 2 x - 3 x^2)^(1/2))/(2 x^2), {x, 0, 50}], x]^3 (* G. C. Greubel, Oct 03 2017 *)

Formula

a(n) = A001006(n)^3.