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A218107 Number of transitive reflexive early confluent binary relations R on n+7 labeled elements with max_{x}(|{y : xRy}|) = n. 2

%I

%S 0,1,608832,378725365,42483670075,2440299822081,106818340013957,

%T 4210378306984993,160415345420268510,6093096859120003590,

%U 234104217274598884642,9167943015777908270142,367520396335132750893274,15117877192137817244318510,638973577773301815522889410

%N Number of transitive reflexive early confluent binary relations R on n+7 labeled elements with max_{x}(|{y : xRy}|) = n.

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

%H Alois P. Heinz, <a href="/A218107/b218107.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = A135313(n+7,n).

%p 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:

%p a:= n-> T(n+7,n): seq (a(n), n=0..20);

%t m = 7; 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 *)

%K nonn

%O 0,3

%A _Alois P. Heinz_, Oct 20 2012

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)