A094731 Number of connected ordered 4-element multiantichains on a labeled n-set.

0, 1, 1, 79, 2101, 63991, 1841461, 45677479, 986583781, 19210969591, 347527345621, 5968468471879, 98788140462661, 1592387628858391, 25181074712937781, 392680081411090279, 6061279724768728741, 92859536016650958391, 1414764491802643937941

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (63,-1701,25887,-245427,1510257,-6084119,15754053,-24891552,21416940,-7484400).

Formula

E.g.f.: exp(15*x) - 12*exp(11*x) + 24*exp(9*x) - 8*exp(7*x) + 27*exp(6*x) - 96*exp(5*x) - 6*exp(4*x) + 246*exp(3*x) - 288*exp(2*x) + 138*exp(x) - 26.

G.f.: x*(1 - 62*x + 1717*x^2 - 27062*x^3 + 285547*x^4 - 1926074*x^5 + 8088135*x^6 - 28645362*x^7 + 105534360*x^8 - 194594400*x^9) / ((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] - 8*Exp[7*x] + 27*Exp[6*x] - 96*Exp[5*x] - 6*Exp[4*x] + 246*Exp[3*x] - 288*Exp[2*x] + 138*Exp[x] - 26, {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(15*x) -12*exp(11*x) +24*exp(9*x) -8*exp(7*x) +27*exp(6*x) -96*exp(5*x) -6*exp(4*x) +246*exp(3*x) -288*exp(2*x) +138*exp(x) -26))) \\ G. C. Greubel, Oct 08 2017
(PARI) concat(0, Vec(x*(1 - 62*x + 1717*x^2 - 27062*x^3 + 285547*x^4 - 1926074*x^5 + 8088135*x^6 - 28645362*x^7 + 105534360*x^8 - 194594400*x^9) / ((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. A094033-A094037, A094729-A094738.

Sequence in context: A231802 A098104 A061997 * A182347 A293919 A205496

Adjacent sequences: A094728 A094729 A094730 * A094732 A094733 A094734

Keyword

nonn,easy

Author

Goran Kilibarda, Vladeta Jovovic, May 24 2004

Status

approved