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A229227
The partition function G(n,10).
3
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213584, 27644267, 190897305, 1382935569, 10479884654, 82861996310, 682044632178, 5832378929502, 51720008131148, 474821737584174, 4506150050048604, 44145239041717738, 445876518513670356
OFFSET
0,3
COMMENTS
Number G(n,10) of set partitions of {1,...,n} into sets of size at most 10.
LINKS
FORMULA
E.g.f.: exp(Sum_{j=1..10} 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, 10):
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, 10)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 22 2016
MATHEMATICA
CoefficientList[Exp[Sum[x^j/j!, {j, 1, 10}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)
CROSSREFS
Column k=10 of A229223.
Cf. A276930.
Sequence in context: A164864 A366776 A192866 * A287589 A287282 A287260
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2013
STATUS
approved