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A193344 Triangle read by rows: T(n,m) (n>=0, 1 <= m <= n+1) = number of unlabeled rigid interval posets with n non-maximal and m maximal elements. 3
1, 1, 1, 1, 3, 2, 2, 9, 13, 6, 5, 32, 72, 69, 24, 16, 132, 409, 605, 432, 120, 61, 623, 2480, 5016, 5498, 3120, 720, 271, 3314, 16222, 41955, 62626, 54370, 25560, 5040, 1372, 19628, 114594, 363123, 690935, 814690, 584580, 234360, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Rows n = 0..50, flattened

Soheir Mohamed Khamis, Exact Counting of Unlabeled Rigid Interval Posets Regarding or Disregarding Height, Order 29, pp. 443-461 (2012).

FORMULA

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

EXAMPLE

Triangle begins

1

1 1

1 3 2

2 9 13 6

5 32 72 69 24

16 132 409 605 432 120

61 623 2480 5016 5498 3120 720

271 3314 16222 41955 62626 54370 25560 5040

1372 19628 114594 363123 690935 814690 584580 ...

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:

T:= (n, m)-> coeff(coeff(w(m+n), z, m), y, n):

seq(seq(T(n, m), m=1..n+1), n=0..10); # Alois P. Heinz, Aug 27 2011

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}]]]]; T[n_, m_] := Coefficient[Coefficient[w[m+n], z, m], y, n]; Table[Table[T[n, m], {m, 1, n+1}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Mar 05 2014, after Alois P. Heinz *)

CROSSREFS

First column is A138265, second column is A194530.

Sequence in context: A091015 A256097 A058147 * A119954 A100804 A143175

Adjacent sequences: A193341 A193342 A193343 * A193345 A193346 A193347

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Aug 26 2011

STATUS

approved

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Last modified December 5 01:43 EST 2022. Contains 358572 sequences. (Running on oeis4.)