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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
OFFSET
3,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 17 2013
STATUS
approved