A094035 Number of connected 4-element antichains on a labeled n-set.

0, 0, 0, 0, 20, 1655, 65305, 1794730, 40179930, 793030245, 14423331635, 248261291960, 4113063835540, 66327037011235, 1049050826515965, 16360528085273190, 252545239130514350, 3869090307434050625, 58948119057416280295, 894447719738683138420

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..845

Formula

E.g.f.: (exp(15*x) - 12*exp(11*x) + 24*exp(9*x) - 14*exp(7*x) + 27*exp(6*x) - 60*exp(5*x) - 24*exp(4*x) + 155*exp(3*x) - 141*exp(2*x) + 50*exp(x) - 6)/4!.

G.f.: 5*x^4*(4+79*x-988*x^2-4414*x^3+52260*x^4-8721*x^5-374220*x^6) / ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-9*x)*(1-11*x)*(1-15*x)). - Colin Barker, Oct 13 2017

Mathematica

With[{nmax = 50}, CoefficientList[Series[(Exp[15*x] - 12*Exp[11*x] + 24*Exp[9*x] - 14*Exp[7*x] + 27*Exp[6*x] - 60*Exp[5*x] - 24*Exp[4*x] + 155*Exp[3*x] - 141*Exp[2*x] + 50*Exp[x] - 6)/4!, {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0, 0, 0, 0], Vec(serlaplace((exp(15*x) -12*exp(11*x) +24*exp(9*x) -14*exp(7*x) +27*exp(6*x) -60*exp(5*x) -24*exp(4*x) +155*exp(3*x) -141*exp(2*x) +50*exp(x) -6)/4!))) \\ G. C. Greubel, Oct 07 2017
(PARI) concat(vector(4), Vec(5*x^4*(4+79*x-988*x^2-4414*x^3+52260*x^4-8721*x^5-374220*x^6) / ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-9*x)*(1-11*x)*(1-15*x)) + O(x^30))) \\ Colin Barker, Oct 13 2017

Crossrefs

Cf. A016269, A047707, A051112-A051118, A094033-A094037.

Sequence in context: A177628 A177626 A177609 * A177614 A177622 A177627

Adjacent sequences: A094032 A094033 A094034 * A094036 A094037 A094038

Keyword

nonn,easy

Author

Goran Kilibarda, Vladeta Jovovic, Apr 22 2004

Status

approved