A218111 Number of transitive reflexive early confluent binary relations R on n+1 labeled elements with max_{x}(|{y : xRy}|) = n.
0, 1, 12, 106, 1035, 11301, 137774, 1863044, 27733869, 451238935, 7972318200, 152065270974, 3115418734415, 68245059703289, 1591993733475570, 39406010771574856, 1031649940977825633, 28483179899706237483, 827159099070697636124, 25205610503231757308450
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..200 (terms n=23..100 from Vincenzo Librandi)
Programs
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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+1,n): seq(a(n), n=0..20);
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Mathematica
t[k_] := t[k] = If[k < 0, 0&, Function[x, Evaluate @ Normal[Series[Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]], {x, 0, k+2}]]]]; tt[k_] := tt[k] = Function[x, (t[k][x]-t[k-1][x]) // Evaluate]; T[n_, k_] := T[n, k] = Coefficient[Series[tt[k][x], {x, 0, n+1}], x, n]*n!; a[n_] := a[n] = T[n+1, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 17 2014, after Maple *)
Formula
a(n) = A135313(n+1,n).
a(n) ~ n! * n^2 / (4 * log(2)^(n+2)). - Vaclav Kotesovec, Nov 20 2021
Comments