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

0,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A000578, A030078, A056570.

Motzkin numbers: A001006.

Sequence in context: A318640 A088038 A061435 * A371988 A098560 A087138

Adjacent sequences: A133051 A133052 A133053 * A133055 A133056 A133057

Keyword

nonn

Author

Omar E. Pol, Oct 30 2007

Status

approved