A133158 Binomial transform of A126568, second binomial transform of A026641.

1, 3, 12, 57, 294, 1578, 8658, 48177, 270774, 1533450, 8736432, 50016090, 287497380, 1658174352, 9591422286, 55618701057, 323225066790, 1882009941570, 10976834700792, 64119701075886, 375057555388884, 2196539772794172, 12878508015774468

Offset

0,2

Comments

The Hankel transform of this sequence is 3^n (see A000244).

Links

Table of n, a(n) for n=0..22.

Isaac DeJager, Madeleine Naquin, Frank Seidl, Colored Motzkin Paths of Higher Order, VERUM 2019.

Formula

Conjecture: 2*n*a(n) + (-19*n+12)*a(n-1) + 6*(8*n-11)*a(n-2) + 36*(-n+2)*a(n-3) = 0. - R. J. Mathar, Jun 30 2013

a(n) ~ 2^(n + 1/2) * 3^(n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Nov 02 2023

Mathematica

CoefficientList[Series[(1 + 3*Sqrt[-1 + 2*x] / Sqrt[-1 + 6*x])/(4 - 6*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Nov 02 2023 *)

Crossrefs

Row sums of triangle in A124575.

Sequence in context: A263667 A101106 A165310 * A328295 A194089 A178807

Adjacent sequences: A133155 A133156 A133157 * A133159 A133160 A133161

Keyword

nonn

Author

Philippe Deléham, Oct 08 2007

Status

approved