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A124504
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Number of partitions of an n-set without blocks of size 3.
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14
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1, 1, 2, 4, 11, 32, 113, 422, 1788, 8015, 39435, 204910, 1144377, 6722107, 41877722, 273328660, 1875326627, 13427171644, 100415636519, 780856389454, 6312398830812, 52891894374481, 459022366424253, 4117482357137214, 38140612800271305, 364280428671552453, 3584042687233836274
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)-1-x^3/6).
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EXAMPLE
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a(3)=4 because if the set is {1,2,3}, then we have 1|2|3, 1|23, 12|3 and 13|2.
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MAPLE
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G:=exp(exp(x)-1-x^3/6): Gser:=series(G, x=0, 30): seq(n!*coeff(Gser, x, n), n=0..26);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=3, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Mar 08 2015, revised, Jun 24 2022
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MATHEMATICA
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a[n_] := SeriesCoefficient[Exp[Exp[x]-1-x^3/6], {x, 0, n}]*n!; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 13 2015 *)
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PROG
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(PARI) x='x+O('x^66); Vec(serlaplace( exp(exp(x)-1-x^3/6) ) ) \\ Joerg Arndt, Jan 19 2015
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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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