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A194530 Number of unlabeled rigid interval posets with n non-maximal and 2 maximal elements. 3
0, 1, 3, 9, 32, 132, 623, 3314, 19628, 128126, 914005, 7074517, 59050739, 528741491, 5055414317, 51406084221, 553946196892, 6305737560455, 75610546284387, 952559077043183, 12579235034203780, 173759983171005721, 2505751777457313815, 37657189917162605826 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

Soheir Mohamed Khamis, Exact Counting of Unlabeled Rigid Interval Posets Regarding or Disregarding Height, Order (journal) (2011).

FORMULA

a(n) = [ y^n z^2 ] W(y,z); W(y,z) = z + z*(W(y,y+z+yz) - W(y,z)).

MAPLE

w:= proc(t) option remember;

      `if`(t=0, 1, expand(convert(series(series(z +z*(subs(

           z=z+y+y*z, w(t-1)) -w(t-1)), z, t+1), y, t+1), polynom)))

    end:

a:= n-> coeff(coeff(w(2+n), z, 2), y, n):

seq(a(n), n=0..50);

MATHEMATICA

w[t_] := w[t] = If[t == 0, 1, Expand[Normal[Series[Series[z+z*((w[t-1] /. z -> z+y+y*z)-w[t-1]), {z, 0, t+1}], {y, 0, t+1}]]]]; a[n_] := a[n] = Coefficient[Coefficient[w[2+n], z, 2], y, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Mar 05 2014, after Alois P. Heinz *)

CROSSREFS

2nd column of A193344.

Column k=2 of A218757.

Sequence in context: A320180 A183425 A039628 * A324238 A005964 A246138

Adjacent sequences:  A194527 A194528 A194529 * A194531 A194532 A194533

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 28 2011

STATUS

approved

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Last modified May 16 22:18 EDT 2021. Contains 343957 sequences. (Running on oeis4.)