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A261238
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Number of transitive reflexive early confluent binary relations R on 2n labeled elements where max_{x}(|{y:xRy}|)=n.
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2
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1, 1, 61, 12075, 4798983, 3151808478, 3085918099231, 4210378306984993, 7631859877504516225, 17735784941946000072572, 51404873131596488549863350, 181773929944698613445522139632, 770224297920086034338727292711511, 3852558194920465350481058381000064850
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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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a(n) ~ c * d^n * n^(2*n), where d = 4.307069427308178... and c = 0.2607079596895... - Vaclav Kotesovec, Nov 20 2021
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MAPLE
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t:= proc(k) option remember; `if`(k<0, 0,
exp(add(x^m/m!*t(k-m), m=1..k)))
end:
A:= proc(n, k) option remember;
coeff(series(t(k), x, n+1), x, n) *n!
end:
a:= n-> A(2*n, n) -A(2*n, n-1):
seq(a(n), n=0..14);
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MATHEMATICA
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t[k_] := t[k] = If[k < 0, 0, Exp[Sum[x^m/m!*t[k-m], {m, 1, k}]]];
A[n_, k_] := A[n, k] = SeriesCoefficient[t[k], {x, 0, n}]*n!;
a[n_] := A[2n, n] - A[2n, n-1];
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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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