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A163942 Fifth right hand column of triangle A163940. 4
1, 14, 121, 834, 5037, 27918, 145777, 728858, 3526933, 16640262, 76952793, 350167122, 1572467389, 6984206846, 30735634369, 134202204426, 582040933605, 2509672804470, 10766469841705, 45982221941570, 195609944400781 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.
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
Equals the fifth right hand column of A163940.
A163941 is another right hand column.
Sequence in context: A002056 A249980 A206635 * A206628 A235710 A239544
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Aug 13 2009
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)