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A218103 Number of transitive reflexive early confluent binary relations R on n+3 labeled elements with max_{x}(|{y : xRy}|) = n. 2
0, 1, 310, 12075, 267715, 5287506, 105494886, 2185028130, 47488375440, 1087116745385, 26234041133443, 666937354457829, 17839235553096685, 501241620987647540, 14769149279798467900, 455566464561064320948, 14685947990441112405726, 493969048893703131221475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.

LINKS

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

FORMULA

a(n) = A135313(n+3,n).

a(n) ~ n! * n^6  / (96 * log(2)^(n+4)). - Vaclav Kotesovec, Nov 20 2021

Conjecture: For fixed k>=0, A135313(n+k,n) ~ n! * n^(2*k)  / (2^(k+1) * k! * log(2)^(n+k+1)). - Vaclav Kotesovec, Nov 20 2021

MAPLE

t:= proc(k) option remember; `if`(k<0, 0,

      unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))

    end:

tt:= proc(k) option remember; unapply((t(k)-t(k-1))(x), x) end:

T:= proc(n, k) option remember;

      coeff(series(tt(k)(x), x, n+1), x, n) *n!

    end:

a:= n-> T(n+3, n):

seq(a(n), n=0..20);

MATHEMATICA

m = 3; f[0, _] = 1; f[k_, x_] := f[k, x] = Exp[Sum[x^m/m!*f[k-m, x], {m, 1, k}]]; (* t = A135302 *) t[0, 0] = 1; t[_, 0] = 0; t[n_, k_] := t[n, k] = SeriesCoefficient[f[k, x], {x, 0, n}]*n!; a[0] = 0; a[n_] := t[n+m, n]-t[n+m, n-1]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 14 2014 *)

CROSSREFS

Sequence in context: A206233 A254972 A237697 * A289304 A281568 A084876

Adjacent sequences:  A218100 A218101 A218102 * A218104 A218105 A218106

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2012

STATUS

approved

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Last modified January 19 22:12 EST 2022. Contains 350466 sequences. (Running on oeis4.)