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 A229245 Number of set partitions of {1,...,n} with largest set of size 3. 2
 1, 4, 20, 90, 420, 2016, 10024, 51640, 276980, 1540440, 8899176, 53313624, 330835960, 2124646720, 14102514560, 96622736256, 682608577104, 4966188238080, 37166169295360, 285813960789280, 2256147419689856, 18263257380872064, 151466260791609600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..500 FORMULA E.g.f.: exp(Sum_{j=1..3} x^j/j!) - exp(Sum_{j=1..2} x^j/j!). MAPLE G:= proc(n, k) option remember; local j; if k>n then G(n, n) elif n=0 then 1 elif k<1 then 0 else G(n-k, k); for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi end: a:= n-> G(n, 3)-G(n, 2): seq(a(n), n=3..30); MATHEMATICA b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[b[n - i j, i - 1] n!/ i!^j/(n - i j)!/j!, {j, 0, n/i}]]]; a[n_] := b[n, 3] - b[n, 2]; a /@ Range[3, 30] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz in A080510 *) CROSSREFS Column k=3 of A080510. Sequence in context: A017965 A180284 A065180 * A328153 A070733 A166175 Adjacent sequences: A229242 A229243 A229244 * A229246 A229247 A229248 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 17 2013 STATUS approved

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Last modified November 29 10:13 EST 2023. Contains 367429 sequences. (Running on oeis4.)