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A229226
The partition function G(n,9).
3
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678558, 4213452, 27642837, 190882290, 1382779413, 10478259030, 82844940414, 681863474058, 5830425411936, 51698581146426, 474582397380708, 4503425395487976, 44113612993755306, 445502134752984696
OFFSET
0,3
COMMENTS
Number G(n,9) of set partitions of {1,...,n} into sets of size at most 9.
LINKS
FORMULA
E.g.f.: exp(Sum_{j=1..9} 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, 9):
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-i)*binomial(n-1, i-1), i=1..min(n, 9)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 22 2016
MATHEMATICA
CoefficientList[Exp[Sum[x^j/j!, {j, 1, 9}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)
CROSSREFS
Column k=9 of A229223.
Cf. A276929.
Sequence in context: A287670 A164863 A192126 * A343671 A276726 A287588
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2013
STATUS
approved