OFFSET
0,3
COMMENTS
Number G(n,7) of set partitions of {1,...,n} into sets of size at most 7.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
E.g.f.: exp(Sum_{j=1..7} 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, 7):
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, 7)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 22 2016
MATHEMATICA
CoefficientList[Exp[Sum[x^j/j!, {j, 1, 7}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2013
STATUS
approved