login
A229225
The partition function G(n,8).
3
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115964, 678448, 4212352, 27632112, 190778186, 1381763398, 10468226150, 82744297014, 680835331228, 5819712427654, 51584619782546, 473344099095848, 4489677962922186, 43957668431564086, 443694809361207824
OFFSET
0,3
COMMENTS
Number G(n,8) of set partitions of {1,...,n} into sets of size at most 8.
LINKS
FORMULA
E.g.f.: exp(Sum_{j=1..8} 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, 8):
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, 8)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 22 2016
MATHEMATICA
CoefficientList[Exp[Sum[x^j/j!, {j, 1, 8}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)
CROSSREFS
Column k=8 of A229223.
Cf. A276928.
Sequence in context: A099263 A366775 A192865 * A343669 A276725 A287587
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2013
STATUS
approved