A094736 Number of connected 4-element multiantichains on a labeled n-set.

0, 1, 1, 13, 189, 3816, 88646, 2013383, 42040699, 807900526, 14537331816, 249111237453, 4119281678909, 66371933499236, 1049372070568186, 16362812045380723, 252561404639492319, 3869204360738213946, 58948921926491795756, 894453362388005059193

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..850

Formula

E.g.f.: (1/4!)*(exp(15*x) -12*exp(11*x) +24*exp(9*x) -2*exp(7*x) +27*exp(6*x) -132*exp(5*x) +12*exp(4*x) +359*exp(3*x) -501*exp(2*x) +314*exp(x)-90).

a(n) = (314-501*2^n+3*2^(2+2n)+359*3^n+2^n*3^(3+n)+8*3^(1+2n)-132*5^n-2*7^n-12*11^n+15^n)/24, n>0. - Benedict W. J. Irwin, May 25 2016

G.f.: x*(1-62*x +1651*x^2 -24816*x^3 +233562*x^4 -1431634*x^5 +5791471*x^6 -15717948*x^7 +28663875*x^8 -28066500*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, May 25 2016

Mathematica

Table[(314 - 501*2^n + 3*2^(2 + 2 n) + 359*3^n + 2^n*3^(3 + n) + 8*3^(1 + 2 n) - 132*5^n - 2*7^n - 12*11^n + 15^n)/ 24 (1 - UnitStep[-n]), {n, 0, 20}] (* Benedict W. J. Irwin, May 25 2016 *)

Prog

(PARI) concat(0, Vec(x*(1-62*x +1651*x^2 -24816*x^3 +233562*x^4 -1431634*x^5 +5791471*x^6 -15717948*x^7 +28663875*x^8 -28066500*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^50))) \\ Colin Barker, May 25 2016

Crossrefs

Cf. A094033-A094037, A094729-A094738.

Sequence in context: A091540 A057799 A057801 * A318595 A055613 A123808

Adjacent sequences: A094733 A094734 A094735 * A094737 A094738 A094739

Keyword

nonn,easy

Author

Goran Kilibarda, Vladeta Jovovic, May 24 2004

Status

approved