A163942 Fifth right hand column of triangle A163940.

1, 14, 121, 834, 5037, 27918, 145777, 728858, 3526933, 16640262, 76952793, 350167122, 1572467389, 6984206846, 30735634369, 134202204426, 582040933605, 2509672804470, 10766469841705, 45982221941570, 195609944400781

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 (14,-75,190,-224,96).

Crossrefs

Equals the fifth right hand column of A163940.

A163941 is another right hand column.

Programs

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2017 *)
LinearRecurrence[{14,-75,190,-224,96},{1,14,121,834,5037},30] (* Harvey P. Dale, Mar 09 2023 *)

PARI

Vec(1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2) + O(x^30)) \\ Michel Marcus, Feb 12 2015

Formula

G.f.: 1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2).

a(n) = (1/18)*(3^(n+6) + (3*n-10)*4^(n+3) - 9*2^(n+3) + 1).

a(n) = 14*a(n-1) - 75*a(n-2) + 190*a(n-3) - 224*a(n-4) + 96*a(n-5).

E.g.f.: (1/18)*( 729*exp(3*x) + 128*(6*x-5)*exp(4*x) - 72*exp(2*x) + exp(x)). - G. C. Greubel, Aug 13 2017