A053442 Moments of generalized Motzkin paths.

1, 0, 2, 1, 6, 6, 21, 30, 82, 141, 342, 650, 1485, 2982, 6612, 13693, 29922, 63072, 136905, 291618, 631302, 1353441, 2928054, 6303798, 13642117, 29454702, 63791456, 138020533, 299191968, 648376932, 1406836717, 3052671816, 6629649798, 14400972413, 31301837952

Offset

2,3

Links

Michael De Vlieger, Table of n, a(n) for n = 2..2919

R. A. Sulanke, Moments of generalized Motzkin paths, J. Integer Sequences, Vol. 3 (2000), #00.1.

Formula

G.f.: 1 / sqrt(1-4*z^2-2*z^3+z^6). - Sean A. Irvine, Dec 25 2021

Mathematica

CoefficientList[Series[1/Sqrt[1 - 4 x^2 - 2 x^3 + x^6], {x, 0, 34}], x], (* Michael De Vlieger, Dec 25 2021 *)

Crossrefs

Sequence in context: A062820 A113336 A113979 * A019082 A345323 A052636

Adjacent sequences: A053439 A053440 A053441 * A053443 A053444 A053445

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jan 12 2000

Extensions

More terms from Reiner Martin, Oct 13 2002

Typos in terms corrected by Sean A. Irvine, Dec 25 2021

Status

approved