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A240799
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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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1
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0, 0, 1, 20, 310, 4660, 72485, 1193080, 20938764, 392485560, 7850724915, 167242351100, 3785057708146, 90775554103052, 2301045251519105, 61499717442074800, 1729026306941190680, 51022485837639054768, 1577126907722325214959, 50967150013960792511700
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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 A001710 (1,3,12,60,360,...).
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, t) option remember; `if`(n=0, [1, 0], add((p-> p+
[0, p[1]*j*(j-1)*t/6])(b(n-j, t+j))*binomial(n, j), j=1..n))
end:
a:= n-> b(n, 0)[2]:
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MATHEMATICA
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b[n_, t_] := b[n, t] = If[n==0, {1, 0}, Sum[Function[p, p+{0, p[[1]]*j*(j-1)*t/6}][b[n-j, t+j]]*Binomial[n, j], {j, 1, n}]]; a[n_] := b[n, 0][[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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