A163941 Fourth right hand column of triangle A163940.

1, 9, 52, 246, 1039, 4083, 15274, 55152, 193957, 668397, 2266816, 7589418, 25143355, 82571751, 269173078, 871958244, 2809322833, 9008574945, 28768068460, 91532284830, 290283189991, 917912770779, 2894936303362

Offset: 0

Author

Johannes W. Meijer, Aug 13 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.
• Index entries for linear recurrences with constant coefficients, signature (9,-29,39,-18).

Crossrefs

Equals the fourth right hand column of A163940.

A163942 is another right hand column.

Programs

Mathematica

LinearRecurrence[{9,-29,39,-18},{1,9,52,246},30] (* or *) CoefficientList[ Series[1/((1-x)(1-2x)(1-3x)^2),{x,0,30}],x] (* Harvey P. Dale, Aug 14 2011 *)

PARI

Vec(1/((1-x)*(1-2*x)*(1-3*x)^2) + O(x^30)) \\ Michel Marcus, Feb 12 2015

Formula

G.f.: 1/((1-x)*(1-2*x)*(1-3*x)^2).

a(n) = (1/4)*(2^(n+5) + (2*n - 3)*3^(n+2) - 1).

a(n) = 9*a(n-1) - 29*a(n-2) + 39*a(n-3) - 18*a(n-4).

E.g.f.: (1/4)*(32*exp(2*x) + 27*(2*x-1)*exp(3*x) - exp(x)). - G. C. Greubel, Aug 13 2017