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A218108
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Number of transitive reflexive early confluent binary relations R on n+8 labeled elements with max_{x}(|{y : xRy}|) = n.
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2
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0, 1, 4910785, 6135529675, 1008618127825, 74564772630777, 3913397076494906, 177779119899659850, 7631859877504516225, 322215964319093498225, 13636766011245325587353, 584294217357391235758011, 25488316708898114509899955, 1135731969645865474902932115
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OFFSET
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0,3
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COMMENTS
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R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
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LINKS
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FORMULA
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MAPLE
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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+8, n): seq (a(n), n=0..20);
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MATHEMATICA
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m = 8; 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-François Alcover, Feb 14 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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