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A218104
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Number of transitive reflexive early confluent binary relations R on n+4 labeled elements with max_{x}(|{y : xRy}|) = n.
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2
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0, 1, 1821, 141533, 4798983, 124878033, 3068829477, 75967708311, 1933688266686, 51075201835515, 1405508547112670, 40356644902123914, 1209368372802130814, 37806870603888974350, 1231961629420423620918, 41802174277488971170242, 1475352032068521550599837
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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+4, n): seq(a(n), n=0..20);
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MATHEMATICA
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m = 4; 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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