OFFSET
0,2
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).
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
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 *)
PROG
(PARI) Vec(1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2) + O(x^30)) \\ Michel Marcus, Feb 12 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Aug 13 2009
STATUS
approved