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A240798
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Total number of occurrences of the pattern 1=2=3 in all preferential arrangements (or ordered partitions) of n elements.
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2
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0, 0, 1, 12, 130, 1500, 18935, 262248, 3972612, 65500200, 1169398065, 22494463860, 464072915878, 10225330604580, 239720548513355, 5959152063448080, 156592569864940040, 4337574220496785680, 126329273251232688069, 3859509516112803668220, 123426111134706786806890
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OFFSET
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1,4
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COMMENTS
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The number that avoid the pattern 1=2=3 is given in A080599.
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LINKS
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FORMULA
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MAPLE
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b:= proc(n) option remember; `if`(n=0, [1, 0], add((p-> p+
[0, p[1]*binomial(j, 3)])(b(n-j))*binomial(n, j), j=1..n))
end:
a:= n-> b(n)[2]:
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MATHEMATICA
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b[n_] := b[n] = If[n==0, {1, 0}, Sum[Function[p, p+{0, p[[1]]*Binomial[j, 3]} ][b[n-j]]*Binomial[n, j], {j, 1, n}]]; a[n_] := b[n][[2]]; Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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