A133053 Squares of Motzkin numbers.

1, 1, 4, 16, 81, 441, 2601, 16129, 104329, 697225, 4787344, 33616804, 240591121, 1750167225, 12912685956, 96454967184, 728405920089, 5554407254841, 42724289649924, 331213938112656, 2585927836376361, 20319806576858481, 160611160909347729, 1276358595300972225

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cyril Banderier, Markus Kuba, Stephan Wagner, and Michael Wallner, Composition schemes: q-enumerations and phase transitions, arXiv:2311.17226 [math.CO], 2023. See p. 7.

Formula

a(n) = A001006(n)^2.

Mathematica

CoefficientList[Series[(1 - x - (1 - 2x - 3x^2)^(1/2))/(2x^2), {x, 0, 50}], x]^2 (* or *) Table[Hypergeometric2F1[(1-n)/2, -n/2, 2, 4], {n, 0, 50}]^2 (* G. C. Greubel, Oct 03 2017 *)

Crossrefs

Cf. A000290, A001248, A007598.

Motzkin numbers: A001006.

Sequence in context: A118997 A337839 A001257 * A342326 A110378 A076997

Adjacent sequences: A133050 A133051 A133052 * A133054 A133055 A133056

Keyword

nonn

Author

Omar E. Pol, Oct 30 2007

Status

approved