|
|
A294084
|
|
Number of indecomposable intervals in the Tamari lattices.
|
|
1
|
|
|
0, 1, 2, 8, 41, 240, 1528, 10312, 72647, 528992, 3954488, 30201504, 234798627, 1853076528, 14814453896, 119763949936, 977709717091, 8050816106176, 66803956281592, 558146870481760, 4692269111973668, 39669049950811328, 337082395954643168, 2877697636252004168, 24672447821197834553
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
This is also the number of interval-posets with connected Hasse diagram.
|
|
LINKS
|
|
|
FORMULA
|
The generating series can be obtained by inverting the generating series of A000260.
|
|
EXAMPLE
|
Among the 3 interval-posets of size 2 :
1 --> 2 ; 1 <-- 2 ; 1 2,
only the third (which is an antichain) is not a connected poset.
|
|
MAPLE
|
h:= proc(n) h(n):= 2*(4*n+1)!/((n+1)!*(3*n+2)!) end:
a:= proc(n) a(n):= `if`(n=0, 0, h(n)-add(a(n-i)*h(i), i=1..n-1)) end:
|
|
MATHEMATICA
|
terms = 25;
G[_] = 0; Do[G[x_] = 1 + x G[x]^4 + O[x]^terms, terms];
F[x_] = 1 - 1/((2 - G[x]) G[x]^2);
|
|
PROG
|
(Sage)
F = PowerSeriesRing(ZZ, 't')([1] + [(2 * binomial(4 * n + 1, n - 1)) // (n * (n + 1)) for n in range(1, 20)])
1 - F.inverse()
(Julia)
using Nemo
s(n) = div(Nemo.binom(4*n + 2, n + 1), (2*n + 1) * (3*n + 2))
R, z = PowerSeriesRing(ZZ, 25, "z")
F = sum(s(n)z^n for n in 0:25)
G = 1 - inv(F)
println([coeff(G, n) for n in 0:24]) # Peter Luschny, Feb 26 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|