A094730 Number of connected ordered 3-element multiantichains on a labeled n-set.

0, 1, 1, 25, 337, 4321, 46681, 437305, 3721537, 29740561, 228000361, 1699890985, 12435686737, 89792976001, 642488104441, 4567920215065, 32331017955937, 228106608326641, 1605738151030921, 11285298643841545, 79223419486529137

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

E.g.f.: exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 17*exp(3*x) - 30*exp(2*x) + 21*exp(x) - 6.

Empirical g.f.: -x*(5040*x^5 - 2686*x^4 + 843*x^3 - 193*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 07 2013

Mathematica

With[{nmax = 50}, CoefficientList[Series[Exp[7*x] - 6*Exp[5*x] + 3*Exp[4*x] + 17*Exp[3*x] - 30*Exp[2*x] + 21*Exp[x] - 6, {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 08 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 17*exp(3*x) - 30*exp(2*x) + 21*exp(x) - 6))) \\ G. C. Greubel, Oct 08 2017

Crossrefs

Cf. A094033-A094037, A094729-A094738.

Sequence in context: A022589 A344656 A199657 * A265930 A265922 A136736

Adjacent sequences: A094727 A094728 A094729 * A094731 A094732 A094733

Keyword

nonn

Author

Goran Kilibarda, Vladeta Jovovic, May 24 2004

Status

approved