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

Author

Philippe Deléham, Oct 08 2007

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Row sums of triangle in A124575.

Programs

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 *)

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