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 A124504 Number of partitions of an n-set without blocks of size 3. 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA E.g.f.: exp(exp(x)-1-x^3/6). a(n) = A124503(n,0). EXAMPLE a(3)=4 because if the set is {1,2,3}, then we have 1|2|3, 1|23, 12|3 and 13|2. MAPLE 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 MATHEMATICA 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 *) PROG (PARI) x='x+O('x^66); Vec(serlaplace( exp(exp(x)-1-x^3/6) ) ) \\ Joerg Arndt, Jan 19 2015 CROSSREFS Cf. A124503, A328153. Sequence in context: A148171 A318644 A113774 * A056324 A056325 A345207 Adjacent sequences: A124501 A124502 A124503 * A124505 A124506 A124507 KEYWORD nonn AUTHOR Emeric Deutsch, Nov 14 2006 STATUS approved

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Last modified November 29 06:00 EST 2022. Contains 358422 sequences. (Running on oeis4.)