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A094735
Number of connected 3-element multiantichains on a labeled n-set.
1
0, 1, 1, 8, 75, 796, 8051, 73788, 623155, 4965836, 38028051, 283400668, 2072874035, 14966280876, 107083717651, 761327161148, 5388524417715, 38017832427916, 267623218488851, 1880883687651228, 13203904989574195, 92616374066478956, 649261556308773651
OFFSET
0,4
LINKS
FORMULA
E.g.f.: (1/3!)*(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 20*exp(3*x) - 39*exp(2*x) + 35*exp(x) - 14).
G.f.: -x*(1960*x^5 - 1695*x^4 + 731*x^3 - 176*x^2 + 21*x - 1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - Colin Barker, Jul 13 2013
a(n) = (7^n - 6*5^n + 20*3^n + 3*4^n - 39*2^n + 35)/6, n > 0. - Benedict W. J. Irwin, May 25 2016
MATHEMATICA
Table[(7^n-6*5^n+20*3^n+3*4^n-39*2^n+35)/6(1-UnitStep[-n]), {n, 0, 20}] (* Benedict W. J. Irwin, May 25 2016 *)
PROG
(PARI) x='x+O('x^50); concat([0], Vec(serlaplace((1/3!)*(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 20*exp(3*x) - 39*exp(2*x) + 35*exp(x) - 14)))) \\ G. C. Greubel, Oct 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Goran Kilibarda, Vladeta Jovovic, May 24 2004
EXTENSIONS
More terms from Colin Barker, Jul 13 2013
STATUS
approved